Centralizers of elementary Abelian subgroups in finite p-groups
نویسندگان
چکیده
منابع مشابه
Finite $p$-groups and centralizers of non-cyclic abelian subgroups
A $p$-group $G$ is called a $mathcal{CAC}$-$p$-group if $C_G(H)/H$ is cyclic for every non-cyclic abelian subgroup $H$ in $G$ with $Hnleq Z(G)$. In this paper, we give a complete classification of finite $mathcal{CAC}$-$p$-groups.
متن کاملfinite $p$-groups and centralizers of non-cyclic abelian subgroups
a $p$-group $g$ is called a $mathcal{cac}$-$p$-group if $c_g(h)/h$ is cyclic for every non-cyclic abelian subgroup $h$ in $g$ with $hnleq z(g)$. in this paper, we give a complete classification of finite $mathcal{cac}$-$p$-groups.
متن کاملLarge Abelian Subgroups of Finite p-Groups
It would be interesting to extend this result by allowing B to have nilpotence class 2 instead of necessarily being abelian. This cannot be done if p = 2 (Example 4.2), but perhaps it is possible for p odd. (It was done by the author ([Gor, p.274]; [HB, III, p.21]) for the special case in which p is odd and [B,B] ≤ A.) However, there is an application of Thompson’s Replacement Theorem that can ...
متن کاملElementary 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...
متن کاملp-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...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1978
ISSN: 0021-8693
DOI: 10.1016/0021-8693(78)90137-0