Order complexes of coset posets of finite groups are not contractible
classification
🧮 math.CO
math.GR
keywords
contractiblefiniteneverorderacyclicbrowncomplexcomplexes
read the original abstract
We show that the order complex of the poset of all cosets of all proper subgroups of a finite group $G$ is never $\mathbb{F}_{2}$-acyclic and therefore never contractible. This settles a question of K. S. Brown.
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