Solitary Solvable Groups

Abstract

A subgroup H of a group G is a solitary subgroup of G if G does not contain another isomorphic copy of H. Combining together the concepts of solitary subgroups and solvable groups, we define (normal) solitary solvable groups and (normal) strongly solitary solvable groups. We derive several results that hold for these groups and we discuss classes of groups that, under certain hypotheses, are (normal) solitary solvable and (normal) strongly solitary solvable. We also derive several results about p-groups that are solitary solvable.

Key Words:

• A-groups
• Solitary subgroups
• Solvable group

2000 Mathematics Subject Classification:

• 20F16

ACKNOWLEDGMENT

The authors would like to thank the referee for the helpful suggestions to strengthen Theorem 5.6.

Notes

Communicated by A. Turull.