Partially ordered sets of non-trivial nilpotent π-subgroups II
Partially ordered sets of non-trivial nilpotent π-subgroups II
复制标题
非平凡幂零子群 II 的偏序集
DOI：
10.1016/j.topol.2017.09.011
复制
发表时间：
2017
影响因子：
0.6
通讯作者：
Nobuo Iiyori and Masato Sawabe
中科院分区：
文献类型：
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作者：
Ito Masahiko;Noumi Masatoshi;飛田明彦;Nobuo Iiyori and Masato Sawabe
设G是有限群，π是整除G阶的素数集合.用N π（G）和L π（G）分别表示G的非平凡幂零π-子群的全和，以及N π（G）中所有子群U的全和，使得O π ZNG（U）≤ U.本文研究了已知具有相同同伦类型的两个偏序集的同伦等价关系。作为应用，我们利用Mayer-Vietoris序列研究了相伴序复形的同调Hn（N π（G））.进一步，我们给出了确定L π（GL（n，pe））的一个算法，其中p <$π.这最终减少到G L（n，pe）的不可约子群的确定。
Let G be a finite group, and π a set of prime numbers dividing the order of G. Denote by N π (G) and L π (G) respectively the totality of non-trivial nilpotent π-subgroups of G, and that of all subgroups U in N π (G) such that O π Z N G (U)≤ 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 H n (N π (G)) of the associated order complex by making use of Mayer–Vietoris sequences. Furthermore, we provide an algorithm for determining L π (G L (n, p e)) where p∉ π. The determination of this is eventually reduced to that of irreducible subgroups of G L (n, p e).