Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5777725 | Topology and its Applications | 2017 | 22 Pages |
Abstract
Let G be a finite group, and Ï a set of prime numbers dividing the order of G. Denote by NÏ(G) and LÏ(G) respectively the totality of non-trivial nilpotent Ï-subgroups of G, and that of all subgroups U in NÏ(G) such that OÏZNG(U)â¤U. In this paper, we study homotopy equivalences related to those two posets which are known to have the same homotopy type. As an application, we deal with homology Hn(NÏ(G)) of the associated order complex by making use of Mayer-Vietoris sequences. Furthermore, we provide an algorithm for determining LÏ(GL(n,pe)) where pâÏ. The determination of this is eventually reduced to that of irreducible subgroups of GL(n,pe).
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
Nobuo Iiyori, Masato Sawabe,