Decomposable Groups Research Articles

Finiteness conditions in the stable module category

We study groups whose cohomology functors commute with filtered colimits in high dimensions. We relate this condition to the existence of projective resolutions which exhibit some finiteness properties in high dimensions, and to the existence of Eilenberg–Mac Lane spaces with finitely many n-cells for all sufficiently large n. To that end, we determine the structure of completely finitary Gorenstein projective modules over group rings. The methods are inspired by representation theory and make use of the stable module category, in which morphisms are defined through complete cohomology. In order to carry out these methods, we need to restrict ourselves to certain classes of hierarchically decomposable groups.

On abelian groups with right-invariant isometries

We describe the reduced periodically complete groups, algebraically compact groups, and torsion-free completely decomposable groups with right-invariant monomorphisms preserving the p-heights of the elements of the group under study.

Computable completely decomposable groups

Computable completely decomposable groups

Microbial regulation of global biogeochemical cycles.

Microbial regulation of global biogeochemical cycles.

Quasi-Endomorphism Rings of Almost Completely Decomposable Torsion-Free Abelian Groups of Rank 4 With Zero Jacobson Radical

In this paper, a description of rings of quasi-endomorphisms of almost completely decomposable torsion-free Abelian groups of rank 4 with zero Jacobson radical is obtained.

On Abelian Groups Close to E-Solvable Groups

E-nilpotent and E-solvable Abelian groups are studied. The properties of such groups are studied, and examples illustrating the differences and connections between the investigated classes of groups are presented. The structure of E-solvable periodical, completely decomposable, coperiodic, split mixed, and other groups is shown.

Determinability of a Completely Decomposable Block-Rigid Torsion-Free Abelian Group by Its Automorphism Group

In this paper, we consider the question of determinability of an Abelian group by its automorphism group in the class of completely decomposable block-rigid torsion-free Abelian groups.

The class of [formula omitted]-groups with homocyclic regulator quotient of exponent [formula omitted] has bounded representation type

The class of almost completely decomposable groups with a critical typeset of type (1,3) and a homocyclic regulator quotient of exponent p4 is shown to be of bounded representation type. There are only nine near-isomorphism types of indecomposables, all of rank ⩽6.

Representations of Posets and Indecomposable Torsion-Free Abelian Groups

Representations of posets in certain modules are used to find indecomposable almost completely decomposable torsion-free abelian groups. For a special class of almost completely decomposable groups we determine the possible ranks of indecomposable groups and show that the possible ranks are realized by indecomposable groups in the class.

Home-Field Advantage: A matter of interaction between litter biochemistry and decomposer biota

Home-Field Advantage (HFA) defines the way with which a plant litter may decompose faster in the habitat from which it derives (i.e. home) than beneath a different plant community (i.e. away from home). Recent studies, using plurispecific litter and involving several soil biota groups, failed to demonstrate a clear positive HFA effect. The interactions between different soil biota groups and different litter types may cause additive effect on decomposition process. Concomitantly, new hypothesis was raised which expects a continuum from positive to negative interactions between transplanted litter and host litter as both litters become increasingly dissimilar in quality, which has been called Substrate quality–Matrix quality Interaction (SMI). Against this background, we aimed at testing the influence of both litter quality and soil organisms in determining the HFA and the SMI hypothesis. We used reciprocal plurispecific transplanting litter along a gradient of litter quality with three successional stages: early (S1), medium (S2) and late successional stage (S3), coupled with litterbags of different mesh size to select different decomposers communities. Furthermore, we analyzed litter quality in order to test the SMI hypothesis. Overall, we did not observe a general HFA or SMI effect. In micromesh litterbags, only S1 litter showed an HFA effect (+7%) while in mesomesh litterbags, only S2 litter presented an HFA effect (+8%). The contribution of each litter quality fraction to the HFA index allowed us to show that only highly labile fractions (i.e., solubles and hemicellulose) presented a positive HFA index, independently of the mesh size. Indeed, our findings corroborated the SMI hypothesis but for labile fraction only. Finally, our results highlighted a strong inertia between different soil decomposer groups for the attack of the most recalcitrant biochemical fraction (i.e. lignin) only in late stage, independently of the litter origin.

Elemental composition and degree of homeostasis of fungi: are aquatic hyphomycetes more like metazoans, bacteria or plants?

Ecological stoichiometry generally assumes that heterotrophs have a higher degree of ele- mental homeostasis than autotrophs. Differences between fixed consumer nutrient requirements and nutrients available in resources allow prediction of the intensity of nutrient recycling ensured by heterotrophs. Despite their fundamental role in detritus decomposition, extremely few data are currently available on fungal elemental composition. In this study, we quantified the degree of elemental homeostasis of aquatic hyphomycetes used as model organisms. Contrary to metazoans, but similar to plants, aquatic hyphomy- cetes exhibited highly plastic elemental compositions. Mycelium also reached far higher C/ nutrient ratios than reported for bacteria. Our results suggest that non-homeostasis of fungi should be explicitly included in stoichiometric models dealing with nutrient recycling, and that the discrepancy in homeostasis between some bacterial strains and fungi should cer- tainly be considered when investigating interactions between both groups of decomposers.

Indecomposable (1,3)-Groups and a matrix problem

Almost completely decomposable groups with a critical typeset of type (1, 3) and a p-primary regulator quotient are studied. It is shown that there are, depending on the exponent of the regulator quotient p k, either no indecomposables if k ⩽ 2; only six near isomorphism types of indecomposables if k = 3; and indecomposables of arbitrary large rank if k ⩾ 4.

High Spatial Resolution Infrared Micro-Spectroscopy Reveals the Mechanism of Leaf Lignin Decomposition by Aquatic Fungi

Organic carbon is a critical component of aquatic systems, providing energy storage and transfer between organisms. Fungi are a major decomposer group in the aquatic carbon cycle, and are one of few groups thought to be capable of breaking down woody (lignified) tissue. In this work we have used high spatial resolution (synchrotron light source) infrared micro-spectroscopy to study the interaction between aquatic fungi and lignified leaf vein material (xylem) from River Redgum trees (E. camaldulensis) endemic to the lowland rivers of South-Eastern Australia. The work provides spatially explicit evidence that fungal colonisation of leaf litter involves the oxidative breakdown of lignin immediately adjacent to the fungal tissue and depletion of the lignin-bound cellulose. Cellulose depletion occurs over relatively short length scales (5–15 µm) and highlights the likely importance of mechanical breakdown in accessing the carbohydrate content of this resource. Low bioavailability compounds (oxidized lignin and polyphenols of plant origin) remain in colonised leaves, even after fungal activity diminishes, and suggests a possible pathway for the sequestration of carbon in wetlands. The work shows that fungi likely have a critical role in the partitioning of lignified material into a biodegradable fraction that can re-enter the aquatic carbon cycle, and a recalcitrant fraction that enters long-term storage in sediments or contribute to the formation of dissolved organic carbon in the water column.

Effectively categorical abelian groups

We study effective categoricity of computable abelian groups of the form ⊕i∈ωH, where H is a subgroup of (Q,+). Such groups are called homogeneous completely decomposable. It is well-known that a homogeneous completely decomposable group is computably categorical if and only if its rank is finite.We study Δn0-categoricity in this class of groups, for n>1. We introduce a new algebraic concept of S-independence which is a generalization of the well-known notion of p-independence. We develop the theory of S-independent sets. We apply these techniques to show that every homogeneous completely decomposable group is Δ30-categorical.We prove that a homogeneous completely decomposable group of infinite rank is Δ20-categorical if and only if it is isomorphic to the free module over the localization of Z by a computably enumerable set of primes P with the semi-low complement (within the set of all primes).We apply these results and techniques to study the complexity of generating bases of computable free modules over localizations of integers, including the free abelian group.

The question of the definability of Abelian groups by the centers of their endomorphism rings

We obtain necessary and sufficient conditions for an Abelian group in the class of completely decomposable torsion-free Abelian groups of a chosen finite rank to be definable in this class by the center of the endomorphism ring of the group.

The FungiResp method: An application of the MicroResp™ method to assess fungi in microbial communities as soil biological indicators

Soil ecosystem services need to monitor soil quality in terms of soil functions. This need in turn requires functional indicators. Microbial functional diversity offers a way to characterize soil quality and any changes to it. Among soil microbial communities, fungi play a critical role in organic matter decomposition and nutrient cycling in soil by decomposing complex substrates, but only a few studies have focused on the function of soil fungal communities. We have developed a protocol based on substrate-induced respiration using the MicroResp™ technique combined with a selective inhibition (SI) procedure to characterize the fungal biomass and catabolic profiles for soil microbial and fungal communities: the FungiResp method. After comparisons with oxytetracycline, we chose bronopol as a bactericide to extend the FungiResp protocol. An optimal bronopol concentration of 78μgg−1 soil was selected for the four soils tested to minimize the risk of inhibiting non-target communities (fungi). We used this convenient, miniaturized method to compare different soils and different perturbations (drought and heat). The FungiResp method gave further data on the fungal part of the microbial substrate-induced respiration in these different contexts. Also, the catabolic structure of microbial and fungal communities measured as pattern of substrate utilization (CLPPs) enabled us to contrast the functional contributions of the decomposer groups in the different soils studied and highlight the functional impacts of the different perturbations applied to them.

ON QUASI-REPRESENTING GRAPHS FOR A CLASS OF B(1)-GROUPS

In this article, we give a characterization theorem for a class of corank{1 Butler groups of the form G(A 1; : : : ; A n). In particular, two groups G and H are quasi-isomorphic if and only if there is a label- preserving bijection ϕ from the edges of T to the edges of U such that S is a circuit in T if and only if ϕ(S ) is a circuit in U , where T; U are quasi-representing graphs for G; H respectively. The terminology group in this article means a torsion-free abelian group. A Butler group is a pure subgroup of anite rank completely decomposable group and a

Responses of soil microbial communities to water stress: results from a meta‐analysis

Soil heterotrophic respiration and nutrient mineralization are strongly affected by environmental conditions, in particular by moisture fluctuations triggered by rainfall events. When soil moisture decreases, so does decomposers' activity, with microfauna generally undergoing stress sooner than bacteria and fungi. Despite differences in the responses of individual decomposer groups to moisture availability (e.g., bacteria are typically more sensitive than fungi to water stress), we show that responses of decomposers at the community level are different in soils and surface litter, but similar across biomes and climates. This results in a nearly constant soil-moisture threshold corresponding to the point when biological activity ceases, at a water potential of about -14 MPa in mineral soils and -36 MPa in surface litter. This threshold is shown to be comparable to the soil moisture value where solute diffusion becomes strongly inhibited in soil, while in litter it is dehydration rather than diffusion that likely limits biological activity around the stress point. Because of these intrinsic constraints and lack of adaptation to different hydro-climatic regimes, changes in rainfall patterns (primary drivers of the soil moisture balance) may have dramatic impacts on soil carbon and nutrient cycling.

Almost completely decomposable groups and unbounded representation type

Almost completely decomposable groups with a regulating regulator and a p-primary regulator quotient are studied. It is shown that there are indecomposable such groups of arbitrarily large rank provided that the critical typeset contains some basic configuration and the exponent of the regulator quotient is sufficiently large.

Evolutionary trade‐offs among decomposers determine responses to nitrogen enrichment

Evolutionary trade-offs among ecological traits are one mechanism that could determine the responses of functional groups of decomposers to global changes such as nitrogen (N) enrichment. We hypothesised that bacteria targeting recalcitrant carbon compounds require relatively high levels of N availability to support the construction costs of requisite extracellular and transport enzymes. Indeed, we found that taxa that used more recalcitrant (i.e. larger and cyclic) carbon compounds were more prevalent in ocean waters with higher nitrate concentrations. Compared to recalcitrant carbon users, labile carbon users targeted more organic N compounds, were found in relatively nitrate-poor waters, and were more common in higher latitude soils, which is consistent with the paradigm that N-limitation is stronger at higher latitudes. Altogether, evolutionary trade-offs may limit recalcitrant carbon users to habitats with higher N availability.