Title: Connected components of the category of elementary abelian $p$-subgroups

Author: Nadia Mazza


Abstract:

We determine the maximal number of conjugacy classes of maximal elementary abelian
subgroups of rank $2$ in a finite $p$-group $G$, for an odd prime
$p$. Namely, it is $p$ if $G$ has rank at least $3$ and it is
$p+1$ if $G$ has rank $2$. More precisely, if $G$ has rank $2$, there are
exactly $1,~2,~p+1$, or possibly $3$ classes for some $3$-groups of maximal
nilpotency class.