Glasnik Matematicki, Vol. 39, No.2 (2004), 235-243.
2-GROUPS WITH A SELF-CENTRALIZING ABELIAN
SUBGROUP OF TYPE (4,2)
Mathematical Institute, University of Heidelberg,
69120 Heidelberg, Germany
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
we describe the structure of the group G in great detail.
In the other case,
there is an open problem.
2000 Mathematics Subject Classification.
Key words and phrases. Finite 2-groups,
self-centralizing subgroups, Frattini subgroups, minimal nonabelian
2-groups, dihedral, semi-dihedral, generalized quaternian 2-groups.
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