Groups Gn Research Articles

On Gottlieb groups G_{n+k}(M(Z^m + Z_2,n)) for k=1,2

We are motivated by [M. Arkowitz. K. Maruyama. J. Math. Soc. Japan, 66(3):735-743, 2014]: "It would be interesting to compute other Gottlieb groups of Moore spaces such as, for example, G{n+1}(M(A,n))" to compute the Gottlieb groups Gn+k(M(ℤm⊕ℤ2,n)) for k=1,2 and m≥1.

Effectiveness, implementation, and monitoring variables of intermittent hypoxic bicycle training in patients recovered from COVID-19: The AEROBICOVID study.

Hypoxic exposure is safely associated with exercise for many pathological conditions, providing additional effects on health outcomes. COVID-19 is a new disease, so the physiological repercussions caused by exercise in affected patients and the safety of exposure to hypoxia in these conditions are still unknown. Due to the effects of the disease on the respiratory system and following the sequence of AEROBICOVID research work, this study aimed to evaluate the effectiveness, tolerance and acute safety of 24 bicycle training sessions performed under intermittent hypoxic conditions through analysis of peripheral oxyhemoglobin saturation (SpO2), heart rate (HR), rate of perceived exertion (RPE), blood lactate concentration ([La-]) and symptoms of acute mountain sickness in patients recovered from COVID-19. Participants were allocated to three training groups: the normoxia group (GN) remained in normoxia (inspired fraction of O2 (FiO2) of ∼20.9%, a city with 526m altitude) for the entire session; the recovery hypoxia group (GHR) was exposed to hypoxia (FiO2 ∼13.5%, corresponding to 3,000m altitude) all the time except during the effort; the hypoxia group (GH) trained in hypoxia (FiO2 ∼13.5%) throughout the session. The altitude simulation effectively reduced SpO2 mean with significant differences between groups GN, GHR, and GH, being 96.9(1.6), 95.1(3.1), and 87.7(6.5), respectively. Additionally, the proposed exercise and hypoxic stimulus was well-tolerated, since 93% of participants showed no or moderate acute mountain sickness symptoms; maintained nearly 80% of sets at target heart rate; and most frequently reporting session intensity as an RPE of "3" (moderate). The internal load calculation, analyzed through training impulse (TRIMP), calculated using HR [TRIMPHR = HR * training volume (min)] and RPE [TRIMPRPE = RPE * training volume (min)], showed no significant difference between groups. The current strategy effectively promoted the altitude simulation and monitoring variables, being well-tolerated and safely acute exposure, as the low Lake Louise scores and the stable HR, SpO2, and RPE values showed during the sessions.

Automorphism towers of groups of homeomorphisms of Cantor space

We show that for any full and sufficiently transitive (i.e., flexible) group G of homeomorphisms of Cantor space, Aut(Aut(G)) = Aut(G). This class contains many generalisations of the Higman-Thompson g roups Gn,r, and the Rational group $${{\cal R}_2}$$ ℛ 2 of Grigorchuk, Nekrashevych, and Sushchanskiĭ. We also demonstrate that for generalisations Tn,r of R. Thompson’s group T, Aut(Aut(Tn,r)) = Aut(Tn,r). In the case of the groups Gn,r and Tn,r our results extend results of Brin and Guzmán for Thompson’s group T, and generalisations of Thompson’s group F.

Average annual total sunspot area in the last 410 yr: the most probable values and limits of their uncertainties

ABSTRACT The aim of this work is to create a long (410-yr) series of average annual total sunspot areas AR – a physically based index of sunspot activity. We use telescopic observations of the AR index in 1832–1868 and 1875–2020, as well as the relationship between AR and long series of sunspot indices SN (international sunspot numbers, version 2.0) and sunspot groups GN (Svalgaard and Schatten’s version of group sunspot numbers). The Royal Greenwich Observatory series after 1976 is extended by the Kislovodsk Mountain Astronomical Station data. When reconstructing AR from SN, it is taken into account that the function AR = f(SN) has a non-linear systematic character and uncertainty associated with the heterogeneity of these indices. Therefore, in addition to modelling the most probable AR values, predictive limits of reconstruction uncertainty are determined. In the interval 1610–1699 we carried out the reconstruction on the basis of the GN series using the previously proposed decomposition in pseudo-phase space (DPS) method. The resulting series NO21y is freely available online. We show that for this series the empirical Gnevyshev–Ohl rule and Waldmeier effect are fulfilled. Wavelet analysis reveals periodicities of 8.4–13.8 yr for the main cycle (with a sharp decrease of the period before the global Maunder and Dalton minima) and a two-component Gleissberg cycle with typical periods of 50–60 and 90–110 yr.

Universal Equivalence of General and Special Linear Groups Over Fields

In this paper, we study universal equivalence of general and special linear groups over fields. We give the following criterion for this relation to hold: two groups Gn(K) and Gm(L) (G = GL, SL, K and L are infinite fields) are universally equivalent if and only if n = m and the fields K and L are universally equivalent.

Invariant Einstein metrics on certain compact semisimple Lie groups

In this paper, we study left invariant Einstein metrics on compact semisimple Lie groups. A new method to construct holonomy irreducible non-naturally reductive Einstein metrics on certain compact semisimple (non-simple) Lie groups is presented. In particular, we show that if G is a classical compact simple Lie group and H is a closed subgroup such that G/H is a standard homogeneous Einstein manifold, then there exist holonomy irreducible non-naturally reductive Einstein metrics on H×G, except for some very special cases. A further interesting result of this paper is that for any compact simple Lie group G, there always exist holonomy irreducible non-naturally reductive Einstein metrics on the compact semisimple Lie groups Gn, for any n≥4.

ON DIRECT PRODUCT pure − 1 − 2 − 3 SUBGROUPS IN ABELIAN GROUP Gn×Gm

In this paper, we shall define new subgroups which are called pure− 1 − 2 − 3 in abelian groups Gn×Gm for all n,m ∈ N which are a family of pure subgroups. In[1],[2]H.M.A.Abdullah gave the some general properties of pure− 1 − 2 − 3 in abelian group G , but here, we shall prove more than properties on this subgroups in Mod Gn×Gm , which are not valid for pure subgroups.

Hardness of computing clique number and chromatic number for Cayley graphs

Computing the clique number and chromatic number of a general graph are well-known NP-Hard problems. Codenotti et al., (1998) showed that computing clique number and chromatic number are both NP-Hard problems for the class of circulant graphs. We show that computing clique number is NP-Hard for the class of Cayley graphs for the groups Gn, where G is any fixed finite group (e.g., cubelike graphs). We also show that computing chromatic number cannot be done in polynomial time (under the assumption NP≠ZPP) for the same class of graphs. Our presentation uses free Cayley graphs. The proof combines free Cayley graphs with quotient graphs and Goppa codes.

The area and absolute magnetic flux of sunspots over the past 400 years

A new series of yearly-mean relative sunspot numbers SN 2 that has been extrapolated into the past (to 1610) is presented. The Kislovodsk series with the scale factor b = 1.0094 ± 0.0059 represents a reasonable continuation of the mean-monthly and mean-yearly total sunspot areas of the Greenwich series after 1976. The second maximum of the 24th solar-activity cycle was not anomalously low, and was no lower than 6 of the past 13 cycles. A series A 2 of values for the total sunspot area in 1610–2015 has been constructed, and is complementary to new versions of the series of the relative number of sunspots SN 2 and the number of sunspot groups GN 2. When needed, this series can be reduced to yield a quantity having a clear physical meaning—the spot absolute magnetic flux Φ Σ(t)[Mx] = 2.16 × 1019 A(t) [mvh]. The maximum sunspot area during the Maunder minimum is much higher in the new series compared to the previous version. This at least partially supports the validity of arguments that cast doubt on the anomalously low ampltude of the solar cycles during the Maunder minimum that has been assumed by many researchers earlier.

The Influence of Oral Carbohydrate Solution Intake on Stress Response before Total Hip Replacement Surgery during Epidural and General Anaesthesia.

The effects of oral carbohydrate solutions, ingested 2 h prior to operation, on stress response were studied in patients undergoing general or epidural anaesthesia. The study was performed on 80 ASA I-II adult patients undergoing elective total hip replacement, which were randomized to four groups (n=20). Group G patients undergoing general anaesthesia fasted for 8 h preoperatively; Group GN patients undergoing general anaesthesia drank oral carbohydrate solutions preoperatively; Group E patients undergoing epidural anaesthesia fasted for 8 h and Group EN patients undergoing epidural anaesthesia drank oral carbohydrate solutions preoperatively. Groups GN and EN drank 800 mL of 12.5% oral carbohydrate solution at 24:00 preoperatively and 400 mL 2 h before the operation. Blood samples were taken for measurements of glucose, insulin, cortisol and IL-6 levels. The effect of preoperative oral carbohydrate ingestion on blood glucose levels was not significant. Insulin levels 24 h prior to surgery were similar; however, insulin levels measured just before surgery were 2-3 times higher in groups GN and EN than in groups G and E. Insulin levels at the 24(th) postoperative hour in epidural groups were increased compared to those at basal levels, although general anaesthesia groups showed a decrease. From these measurements, only the change in Group EN was statistically significant (p<0.05). Plasma cortisol levels at the 2(nd) peroperative hour were higher in epidural groups than in general anaesthesia groups. Both anaesthesia techniques did not have an effect on IL-6 levels. We concluded that epidural anaesthesia suppressed stress response, although preoperative oral carbohydrate nutrition did not reveal a significant effect on surgical stress response.

Subgroups of the group of homeomorphisms of the Cantor space and a duality between a class of inverse monoids and a class of Hausdorff étale groupoids

Under non-commutative Stone duality, there is a correspondence between second countable Hausdorff étale groupoids which have a Cantor space of identities and what we call Tarski inverse monoids: that is, countable Boolean inverse ∧-monoids with semilattices of idempotents which are countable and atomless. Tarski inverse monoids are therefore the algebraic counterparts of the étale groupoids studied by Matui and provide a natural setting for many of his calculations. Under this duality, we prove that natural properties of the étale groupoid correspond to natural algebraic properties of the Tarski inverse monoid: effective groupoids correspond to fundamental Tarski inverse monoids and minimal groupoids correspond to 0-simplifying Tarski inverse monoids. Particularly interesting are the principal groupoids which correspond to Tarski inverse monoids where every element is a finite join of infinitesimals and idempotents. Here an infinitesimal is simply a non-zero element with square zero. The groups of units of fundamental Tarski inverse monoids generalize the finite symmetric groups and include amongst their number the Thompson groups Gn,1 as well as the groups of units of AF inverse monoids, Krieger's ample groups being examples.

Desempenho produtivo e econômico de três grupos genéticos de bovinos recriados a pasto com suplementação e terminados em confinamento

Avaliou-se o desempenho produtivo e econômico de três grupos genéticos de bovinos em sistema com recria a pasto e terminação em confinamento, com ciclo de produção de um ano. Foram utilizados 36 bovinos não castrados, com média de 270±50 dias de idade e peso médio inicial de 241,3±34kg, sendo 12 Guzolandos (1/2 Guzerá x 1/2 Holandês), 12 Guzonel (1/2 Guzerá x 1/2 Nelore) e 12 Tricross (1/2 Simental x 1/2 Guzonel). O delineamento estatístico foi inteiramente ao acaso. Os animais permaneceram em pastejo rotacionado de Brachiaria brizantha cv. Marandu, com suplementação comercial; na terminação, receberam dieta composta por silagem de sorgo e concentrado (50:50) durante 61 dias. Os índices de desempenho avaliados foram o ganho médio de peso diário (GMD), ganho médio de peso no período, peso corporal final e, como indicadores econômicos, a receita total, custo operacional total por arroba (COT/@), margem bruta e margem líquida. O GMD na recria foi semelhante (P&gt;0,05) entre os grupos que apresentaram média de 746 e 456 gramas, respectivamente, para os períodos águas/transição águas-seca e seca. O COT/@ da recria do grupo Tricross (R$69,44) foi superior aos dos grupos Guzonel (R$66,75) e Guzolando (R$ 64,86). No período de terminação, o GMD foi semelhante entre os grupamentos, apresentanto o valor médio de 1,55kg. O COT/@ da terminação em confinamento foi R$ 91,48, R$114,15 e R$122,78, para Tricross, Guzonel e Guzolando, respectivamente. Considerando-se o sistema de ciclo curto completo, obteve-se COT/@ menor para o grupamento Tricross (R$77,92), seguido pelo grupamento Guzonel (R$ 74,89) e Guzolando (R$ 78,43). Nas condições de produção avaliadas, o grupo Tricross foi o mais eficiente economicamente.

A family of polycyclic groups over which the uniform conjugacy problem is NP-complete

In this paper, we study the conjugacy problem in polycyclic groups. Our main result is that we construct polycyclic groups Gn whose conjugacy problem is at least as hard as the subset sum problem with n indeterminates. As such, the uniform conjugacy problem over the groups Gn is NP-complete where the parameters of the problem are taken in terms of n and the length of the elements given on input.

Infection by string links and new structure in the knot concordance group

This paper highlights the importance of string link concordance in the understanding of knot concordance in general. The results of this paper show that there are infinitely many nontrivial knots in the groups Gn of n‐solvable knots modulo n:5‐solvable knots, for n greater than or equal to 2, which are not concordant to any knot that is obtained by two or more iterated infections of an Arf invariant zero knot by knots. This latter class accounts for nearly all previously known examples of knots in Gn , n greater than or equal to 2. In this paper we will generalize the concept of when a rational Laurent polynomial is strongly coprime to another, first introduced by Cochran, Harvey and Leidy, to include multivariable polynomials. We also prove the existence of multivariable polynomials which are strongly coprime to all single variable Laurent polynomials. From this definition of coprimality we define the derived series localized at M for a given sequence of multivariable polynomials M. From such series we obtain refinements of the n‐solvable filtration. The operation of infection by a string link is then used to demonstrate that for particular M, certain quotients of successive terms of these refined filtrations have infinite rank. 57M25; 20J05

Representation theory and homological stability

We introduce the idea of representation stability (and several variations) for a sequence of representations Vn of groups Gn. A central application of the new viewpoint we introduce here is the importation of representation theory into the study of homological stability. This makes it possible to extend classical theorems of homological stability to a much broader variety of examples. Representation stability also provides a framework in which to find and to predict patterns, from classical representation theory (Littlewood–Richardson and Murnaghan rules, stability of Schur functors), to cohomology of groups (pure braid, Torelli and congruence groups), to Lie algebras and their homology, to the (equivariant) cohomology of flag and Schubert varieties, to combinatorics (the (n+1)n−1 conjecture). The majority of this paper is devoted to exposing this phenomenon through examples. In doing this we obtain applications, theorems and conjectures.Beyond the discovery of new phenomena, the viewpoint of representation stability can be useful in solving problems outside the theory. In addition to the applications given in this paper, it is applied by Church–Ellenberg–Farb (in preparation) [20] to counting problems in number theory and finite group theory. Representation stability is also used by Church (2012) [19] to give broad generalizations and new proofs of classical homological stability theorems for configuration spaces on oriented manifolds.

Diameters of Chevalley groups over local rings

Let G be a Chevalley group scheme of rank l. Let $${G_n := G(\mathbb{Z} / p^{n} \mathbb{Z})}$$ be the family of finite groups for $${n \in \mathbb{N}}$$ and some fixed prime number p > p 0. We prove a uniform poly-logarithmic diameter bound of the Cayley graphs of G n with respect to arbitrary sets of generators. In other words, for any subset S which generates G n , any element of G n is a product of C n d elements from $${S \cup S^{-1}}$$ . Our proof is elementary and effective, in the sense that the constant d and the functions p 0(l) and C(l, p) are calculated explicitly. Moreover, we give an efficient algorithm for computing a short path between any two vertices in any Cayley graph of the groups G n .

NON-COMMUTATIVE STONE DUALITY: INVERSE SEMIGROUPS, TOPOLOGICAL GROUPOIDS AND C*-ALGEBRAS

We study a non-commutative generalization of Stone duality that connects a class of inverse semigroups, called Boolean inverse ∧-semigroups, with a class of topological groupoids, called Hausdorff Boolean groupoids. Much of the paper is given over to showing that Boolean inverse ∧-semigroups arise as completions of inverse ∧-semigroups we call pre-Boolean. An inverse ∧-semigroup is pre-Boolean if and only if every tight filter is an ultrafilter, where tight filters are defined by combining ideas of both Exel and Lenz. A simple necessary condition for a semigroup to be pre-Boolean is derived and a variety of examples of inverse semigroups are shown to satisfy it. Thus the polycyclic inverse monoids, and certain Rees matrix semigroups over the polycyclics, are pre-Boolean and it is proved that the groups of units of their completions are precisely the Thompson–Higman groups Gn, r. The inverse semigroups arising from suitable directed graphs are also pre-Boolean and the topological groupoids arising from these graph inverse semigroups under our non-commutative Stone duality are the groupoids that arise from the Cuntz–Krieger C*-algebras. An elementary application of our theory shows that the finite, fundamental Boolean inverse ∧-semigroups are just the finite direct products of finite symmetric inverse monoids. Finally, we explain how tight filters are related to prime filters setting the scene for future work.

INDUCING W-GRAPHS FOR SYMMETRIC GROUPS

The W-graph representations for symmetric groups Gn and their Hecke algebras have been studied by many authors, but the situation for a large n (for instance n ≥ 16) has not been completely solved. The aim of this note is to provide an algorithm of "inducing W-graphs" step by step from smaller n, to construct W-graphs for the left cells of the symmetric groups for bigger n.

The C*-algebras of the Heisenberg group and of thread-like Lie groups

We describe the C*-algebras of the Heisenberg group Hn, n ≥ 1, and the thread-like Lie groups GN, N ≥ 3, in terms of C*-algebras of operator fields.

Biological parameters of larvae, nymphs, and engorged females of Amblyomma cajennense (Fabricius, 1787) (Acari: Ixodidae) obtained from artificial and successive infestations on Oryctolagus cuniculus (Linnaeus, 1758) (Lagomorpha: Ochotonidae)

The development of acquired resistance to Amblyomma cajennense ticks was evaluated. A total of 18 rabbits were uniformly distributed into three groups named GL, GN, and GA that were submitted to three consecutive infestations with, respectively, larvae, nymphs, and adults of A. cajennense. After the infestations, the parasitic and reproductive parameters of recovered instars were evaluated. A significant reduction of recovery rates of inoculated ticks was observed only after the third infestation of animals in groups GL and GN (P&lt;0.01). The modal day for drop-off of engorged larvae and nymphs increased along the infestations. The recovered engorged nymphs presented a significant reduction of the mean body weight between the first and the third infestations (P&lt;0.01). A significant reduction in the mean recovery rate of engorged females was only observed during the third infestation. However, significant reductions (P&lt;0.05) in body weight, egg mass weight, and larva eclosions were observed for recovered engorged females after the second infestation onwards. The results suggest the occurrence of resistance of rabbits to A. cajennense infestations, being more evident against the adult stage.