On elementary abelian TI-subgroups

The Poset of Elementary Abelian Subgroups Of

If p is a prime number, the poset of all nontrivial elementary abelian p -subgroups of a finite group plays an important role in both group theory and representation theory. It was studied by Quillen [9], who proved among many other things that it is homotopy equivalent to the poset of all nontrivial p -subgroups. In the case of a p -group P , one might believe that this poset has no interest s...

Elementary Abelian Subgroups in p - Groups of Class 2 THÈSE

All the results in this work concern (finite) p-groups. Chapter 1 is concerned with classifications of some classes of p-groups of class 2 and there are no particularly new results in this chapter, which serves more as an introductory chapter. The “geometric” method we use for these classifications differs however from the standard approach, especially for p-groups of class 2 with cyclic center...

p-GROUPS WITH MAXIMAL ELEMENTARY ABELIAN SUBGROUPS OF RANK 2

Let p be an odd prime number and G a finite p-group. We prove that if the rank of G is greater than p, then G has no maximal elementary abelian subgroup of rank 2. It follows that if G has rank greater than p, then the poset E(G) of elementary abelian subgroups of G of rank at least 2 is connected and the torsion-free rank of the group of endotrivial kG-modules is one, for any field k of charac...

On non-normal non-abelian subgroups of finite groups

‎In this paper we prove that a finite group $G$ having at most three‎ ‎conjugacy classes of non-normal non-abelian proper subgroups is‎ ‎always solvable except for $Gcong{rm{A_5}}$‎, ‎which extends Theorem 3.3‎ ‎in [Some sufficient conditions on the number of‎ ‎non-abelian subgroups of a finite group to be solvable‎, ‎Acta Math‎. ‎Sinica (English Series) 27 (2011) 891--896.]‎. ‎Moreover‎, ‎we s...

On N-high Subgroups of Abelian Groups