Hypersolvable Groups

Abstract

Call a group G hypersolvable if it has an ascending series with G/C_G(A) solvable for each factor A of the series. In this article we establish some basic facts about hypersolvable groups. We also prove that if G is a perfect Fitting p-group such that every proper subgroup is contained in a proper normal subgroup, then G has a proper non-hypersolvable subgroup.

Key Words:

• Commutator
• Fitting p-groups
• Hypersolvable
• Nilpotent
• Solvable
• Variety of groups

Mathematics Subject Classification:

• 20F19
• 20E34
• 20E10

ACKNOWLEDGMENTS

This article has been written while the first author was visiting in Michigan State University. He is grateful to Professor Jonathan I. Hall and Professor Ulrich Meierfrankenfeld for their warm hospitality and many helpful discussions. He is also grateful to Gazi University for the financial support and the nice organization.

Notes

Communicated by M. Dixon.