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.
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页码：758 / 773
页数：16
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