1
$\begingroup$

Let $G$ a finite group and $L(G)$ it's lattice of non trivial subgroups. Is it true that the quotient space $|L(G)|/G$ is contractible, where $|L(G)|$ is the geometric simplicial complex associated to the poset $L(G)$ and where the action of $G$ on the poset $L(G)$ is by conjugation ?

Improve this question
$\endgroup$
1
  • 2
    $\begingroup$ Assuming that $L(G)$ is the poset of proper non-trivial subgroups of $G$, the answer is no. For example if $G={\mathbb Z}/6$, $|L(G)|/G$ consists of two points. $\endgroup$
    – Gregory Arone
    Commented Mar 8, 2017 at 15:40

0

Reset to default

You must log in to answer this question.