Subgroup Decomposition Research Articles

Some split exact sequences in the cohomology of groups

We analyze the split exact sequences of (co)homology groups associated to the spaces of Dwyer which give rise to the centralizer decomposition and subgroup decomposition of the classifying space BG of a finite group. In the first instance these sequences have infinite length. We show that they give rise to finite sequences which are also split and exact. The sequences arise as the first page of a spectral sequence.

The impact of unemployment on inequality and poverty in OECD countries

The purpose of this research is to examine the contribution of unemployment to income inequality and poverty in various OECD countries. These relationships have been explored using Luxembourg Income Study micro‐data. Considerable differences across OECD countries are revealed through the use of within‐household unemployment distributions. These differences help to explain most of the observed divergences in the relationship between unemployment and income distribution, in conjunction with the heterogeneous influence of social benefits on the economic position of the unemployed in these countries. A sub‐group decomposition analysis corroborates the limited effect of unemployment on income distribution in most of the considered countries. However, it seems clear that the unemployed are among those with the highest risk of experiencing poverty.JEL classification: D31, I32, J31.

Balanced and Cobalanced Butler Groups

The class of Butler groups—pure subgroups of finite-rank torsion-free completely decomposable groups—has been widely studied by abelian group theorists. Here we present several classification results for groups in two chains of special subclasses of the Butler groups, the K(n)- and co-K(n)-groups. The classes K(n) and co-K(n),n≥1, are defined by balanced and cobalanced exact sequences of Butler groups, respectively. We give direct sum decompositions of certain pure subgroups of K(n)-groups and certain torsion-free quotients of co-K(n)-groups. The direct sum decompositions characterize the groups in those classes and extend some well-known results for Butler groups.

An Anatomy of the Sen and Sen-Shorrocks-Thon Indices: Multiplicative Decomposability and Its Subgroup Decompositions

This paper proposes a new and unified framework for the Sen and Sen-Shorrocks-Thon indices of poverty intensity, which shows an explicit connection between the two indices and the underlying social evaluation function. This paper also identifies the common multiplicative decomposition of the two indices. This allows simple and similar geometric interpretations, easy numerical computation, and common subgroup decompositions, which are useful to policy analysts but not possible prior to the multiplicative decomposition.

Enumeration and Symmetry of Substitution Isomers

A simple group-theoretical approach, which is based on the subgroup decomposition of the isomer permutation representation, is applied to enumerate the substitution isomers of three fullerene cages, D2-C76, D2-C84, and D2d-C84. Several rules governing the symmetry distribution of substitution isomers are extracted from the enumeration results. These rules are also applicable to other substitution frameworks.

Direct decompositions of ideals and normal subgroups

Direct decompositions of ideals and normal subgroups

Source and Subgroup Decomposition Inequalities for the Lorenz Curve

investigated. One of the major research areas in this branch of economics has been inequality decomposition. The fundamental issue is, given total inequality, does this total break down over separate groups or separate income sources? It is clearly of interest to the policymaker to be able to identify the regions or sources that make substantial contributions to total inequality. This question has an interesting converse, which is the question of inequality aggregation. For each of these questions, the derivations of relationhsips between total inequality measures and inequality measures on constituent parts will be necessary for the purposes of computation, or for providing upper or lower bounds on a given (unknown) measure. Many authors have considered source and subgroup decompositions for measures of income inequality.2 However, except for Anand and Kanbur (unpublished) there appears to be little work done on source and subgroup decompositions for the Lorenz curve. Since results for Lorenz curves usually imply results for inequality measures, we investigate Lorenz decompositions in this note. We derive a source decomposition inequality for the Lorenz curve and apply

Construction of grand unified models under maximal subalgebras

A construction of grand unified models of the strong, weak and electromagnetic interactions is described based on the transformation properties of the group generators under a maximal subgroup decomposition without recourse to large representation matrices or to the specific algebraic structures of some classical Lie-groups, such as the Clifford algebra associated with the orthogonal groups or the octonionic structure of the exceptional groups. To illustrate the procedure an explicit construction is given of the SU(5) model useful in the discussion of higher rank groups, of SO(10) under the maximal subalgebras SU(2) L × SU(2) R × SU(4) c and SU(5) × U(1) r and of the exceptional group E 6 under SU(3) L × SU(3) R × SU(3) c and SO(10) × U(1) t . The construction procedure can be used as well with any classical Lie-group.

Primary Groups Whose Basic Subgroup Decompositions can be Lifted

AbstractA primary group G is said to be a l.i.b. group if every idempotent endomorphism of every basic subgroup of G can be extended to an endomorphism of G. We establish the following characterization: A primary group is a l.i.b. group if and only if it is the direct sum of a torsion complete group and a divisible group. The technique used consists of a close analysis of certain subgroups of Prufer-like primary groups.

Branching rules for U(N)⊃U(M) and the evaluation of outer plethysms

Littlewood's third method of evaluating plethysms is generalized by noting that plethysms determine the branching rules associated with the subgroup decomposition U(N)⊃U(M), and by making use of the well-known branching rule for U(M)⊃U(M−1). This generalization leads to recurrence formulas which are simpler than those due to Murnaghan and to a new method of evaluating plethysms which is free of the ambiguities inherent in the use of Littlewood's third method.