CZ-groups (CROSBI ID 229826)
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Tabak, Kristijan ; Pavčević, Mario Osvin
engleski
CZ-groups
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.
p-group ; center ; centralizer ; Frattini subgroup ; minimal nonabelian subgroup
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