Groups with a Finite Number of Normalizer Subgroups

Abstract

The groups having exactly one normalizer are well-known. They are the Dedekind groups. All finite groups having exactly two normalizers were classified by M. D. Pérez-Ramos and, in a recent paper, S. Camp-Mora generalized that result to locally finite groups. In this paper, we will characterize arbitrary groups with a finite number of normalizers and we will investigate the properties of arbitrary groups with two, three and four normalizers.

Key Words:

• Normalizer subgroups
• Central-by-finite groups

Mathematics Subject Classification:

• 20E34
• 20F18
• 20F50

Acknowledgments

Notes

^#Communicated by M. Dixon.