Naslov
CZ-groups

Autori
Tabak, Kristijan ; Pavčević, Mario Osvin

Izvornik
Glasnik matematički (0017-095X) 51(71) (2016); 345-358

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

Ključne riječi
p-group ; center ; centralizer ; Frattini subgroup ; minimal nonabelian subgroup

Sažetak
We describe some aspects of the structure of nonabelian p-groups G for which every nonabelian subgroup has a trivial centralizer in G, i.e. only it's center. We call such groups CZ-groups. The problem of describing the structure of all CZ-groups was posted as one of the first research problems in the open problems list in Yakov Berkovich's book 'Groups of prime power order' Vol 1 [1]. Among other features of such groups, we prove that a minimal CZ-group must contain at least p^5 elements. The structure of maximal abelian subgroups of these groups is described as well.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA