Order complexes of coset posets of finite groups are not contractible

被引：15

作者：

Shareshian, John ^{[2
]}

Woodroofe, Russ ^{[1
]}

机构：

[1] Mississippi State Univ, Dept Math & Stat, Mississippi State, MS 39762 USA

[2] Washington Univ, Dept Math, St Louis, MO 63130 USA

来源：

ADVANCES IN MATHEMATICS | 2016年 / 291卷

基金：

美国国家科学基金会;

关键词：

Order complex; Coset poset; Finite group; Smith Theory; PROBABILISTIC ZETA-FUNCTION; PRIMITIVE PERMUTATION-GROUPS; EULER CHARACTERISTICS; (NON-)CONTRACTIBILITY; SUBGROUPS;

D O I：

10.1016/j.aim.2015.10.018

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that the order complex of the poset of all cosets of all proper subgroups of a finite group G is never F-2-acyclic and therefore never contractible. This settles a question of K.S. Brown. (C) 2015 Published by Elsevier Inc.

引用

页码：758 / 773

页数：16

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