منابع مشابه
On the socles of characteristic subgroups of Abelian p-groups
Fully invariant subgroups of an Abelian p-group have been the object of a good deal of study, while characteristic subgroups have received somewhat less attention. Recently the socles of fully invariant subgroups have been studied and this led to the notion of a socle-regular group. The present work replaces the fully invariant subgroups with characteristic ones and leads in a natural way to th...
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In this paper, we describe the theory and implementation of algorithms for computing chief series, composition series and socles in large permutation groups. The theory is valid for permutation degrees up to 10 000 000. Most parts of the algorithms have been implemented within the Magma Computational Algebra System (Bosma and Cannon, 1993; Bosma et al., 1994; Bosma et al., 1997; Cannon and Play...
متن کاملSocles of Buchsbaum modules, complexes and posets
The socle of a graded Buchsbaum module is studied and is related to its local cohomology modules. This algebraic result is then applied to face enumeration of Buchsbaum simplicial complexes and posets. In particular, new necessary conditions on face numbers and Betti numbers of such complexes and posets are established. These conditions are used to settle in the affirmative Kühnel’s conjecture ...
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We discuss two classes of acyclic groups that are commutator subgroups of finitely presented groups with infinite cyclic abelianization. The first is algebraic and includes groups first exhibited by Baumslag & Gruenberg, of which it is shown that Epstein’s acyclic group is a special case. The second class is geometric, and is shown to include a number of wild arc groups in the literature. 0. In...
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We present geometric conditions on a metric space (Y, dY ) ensuring that almost surely, any isometric action on Y by Gromov’s expander-based random group has a common fixed point. These geometric conditions involve uniform convexity and the validity of nonlinear Poincaré inequalities, and they are stable under natural operations such as scaling, Gromov-Hausdorff limits, and Cartesian products. ...
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ژورنال
عنوان ژورنال: Tohoku Mathematical Journal
سال: 1968
ISSN: 0040-8735
DOI: 10.2748/tmj/1178243079