Connected components of the category of elementary abelian p-subgroups

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.