Naslov
On maximal abelian subgroups in finite 2-groups

Autori
Janko, Zvonimir

Izvornik
Mathematische Zeitschrift (0025-5874) 258 (2008); 629-635

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
finite 2-groups of maximal class; metacyclic 2-groups; minimal non-abelian p-groups; central products

Sažetak
We determine here up to isomorphism the structure of any finite nonabelian 2-group G in which every two distinct maximal abelian subgroups have cyclic intersection. We obtain five infinite classes of such 2-groups (Theorem 1.1). This solves for p=2 the problem Nr. 521 stated by Berekovich (in preparation). The more general problem Nr. 258 stated by Berkovich (in preparation) about the structure of finite nonabelian p-groups G such that the intersection between A and B is equal to Z(G) for every two distinct maximal abelian subgroups A and B is treated in Theorems 3.1 and 3.2. In Corollary 3.3 we get a new result for an arbitrary finite 2-group. As an application of Theorems 3.1 and 3.2, we solve for p=2 a problem of Heineken-Mann (Problem Nr.169 stated in Berkovich, in preparation), classifying finite 2-groups G such that A/Z(G) is cyclic for each maximal abelian subgroup A (Theorem 4.1).

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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

POVEZANOST RADA