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.
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
SEZER, SEZGİN and WAALL, ROBERT W. VAN DER (2006) "Finite Groups all of Whose Abelian Subgroups of Equal Order are Conjugate," Turkish Journal of Mathematics: Vol. 30: No. 2, Article 3. Available at: https://journals.tubitak.gov.tr/math/vol30/iss2/3