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Connected components of the category of elementary abelian $p$-subgroups.

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<mark>Journal publication date</mark>15/12/2008
<mark>Journal</mark>Journal of Algebra
Issue number12
Number of pages7
Pages (from-to)4242-4248
Publication StatusPublished
<mark>Original language</mark>English


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.

Bibliographic note

The final, definitive version of this article has been published in the Journal, Journal of Algebra 320 (12), 2008, © ELSEVIER.