Glasnik Matematicki, Vol. 39, No.2 (2004), 235-243.

2-GROUPS WITH A SELF-CENTRALIZING ABELIAN SUBGROUP OF TYPE (4,2)

Zvonimir Janko

Abstract.   In this paper we classify finite 2-groups G which possess a self-centralizing abelian subgroup A of type (4,2). In the difficult case, where A is contained in the Frattini subgroup Φ(G), we describe the structure of the group G in great detail. In the other case, where A Φ(G), there is an open problem.

2000 Mathematics Subject Classification.   20D15.

Key words and phrases.   Finite 2-groups, self-centralizing subgroups, Frattini subgroups, minimal nonabelian 2-groups, dihedral, semi-dihedral, generalized quaternian 2-groups.