Finite Groups all of Whose Abelian Subgroups of Equal Order are Conjugate

Authors: SEZGİN SEZER, ROBERT W. VAN DER WAALL

Abstract: In this paper we classify the finite groups whose abelian subgroups of equal order (B^*-groups) are conjugate. The classification has been achieved by means of a lot of general structure properties of B^*-groups, provided in the course of the paper.

Keywords: Finite solvable groups, finite non-solvable groups, conjugacy classes of abelian subgroups, projective special linear groups over a finite field, simple first group of Janko, alternating groups, Sylow subgroups, Hall subgroups, Fitting subgroups, transitive action of groups on groups

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