Izvorni znanstveni članak

https://doi.org/10.3336/gm.51.2.05

CZ-groups

Kristijan Tabak orcid.org/0000-0002-7030-4945 ; Rochester Institute of Technology, Zagreb Campus, D.T. Gavrana 15, 10000 Zagreb , Croatia
Mario Osvin Pavčević ; Department of applied mathematics, Faculty of Electrical Engineering and Computing , University of Zagreb , 10 000 Zagreb, Croatia

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 p5 elements. The structure of maximal abelian subgroups of these groups is described as well.

Ključne riječi

p-group, center; centralizer; Frattini subgroup; minimal nonabelian subgroup

Hrčak ID:

170041

URI

https://hrcak.srce.hr/170041

Datum izdavanja:

3.12.2016.

Posjeta: 631 *