engleski

On minimal non-abelian subgroups in finite p-groups

We solve Problem 757 of Berkovich /1/. We also classify the non-abelian finite p-groups g such that whenever A is a maximal subgroup of any minimal non-abelian subgroup H in G, then A is also a maximal abelian subgroup in G (Theorem 1.2), and this solves another problem of Berkovich /1/. Finally, we generalize a result of Blackburn /4/ concerning finite p-groups in which the non-normal subgroups have non-trivial intersection (Theorem 1.3 and Corollary 1.4).

minimal non-abelian p-groups; metacyclic p-groups; special 2-groups; p-groups of maximal class

Istraživač na projektu Zvonimir Janko nema matični broj znanstvenika u R. Hrvatskoj. On je pripadnik hrvatske dijaspore u Heidelbergu, Njemačka.