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

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.

Anahtar Kelimeler:

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, tran

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

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, tran,

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Department of Mathematics and Computer Sciences, C¸ ankaya University, ¨ Ogretmenler Cad. No 14, Balgat Ankara-TURKEY e-mail: sezgin@cankaya.edu.tr Robert W. van der WAALL Korteweg - de Vries Instituut voor Wiskunde, Universiteit van Amsterdam, Plantage Muidergracht 24, TV Amsterdam-NEDERLAND e-mail: waallr@science.uva.nl