Finite non-nilpotent groups with few non-normal non-cyclic subgroups

Mousavi, Hamid; Rezazadeh, Zahra

doi:10.22108/ijgt.2017.21222

Finite non-nilpotent groups with few non-normal non-cyclic subgroups

Document Type : Research Paper

Authors

Hamid Mousavi ¹
Zahra Rezazadeh ²

¹ Department of‎ ‎Mathematical Sciences, ‎University of Tabriz‎, ‎P.O.Box 51666-16471‎, ‎Tabriz‎, ‎Iran

² Department of‎ ‎Mathematical Sciences‎, ‎Isfahan University of Technology‎, ‎P.O.Box 84156-83111‎, ‎Isfahan‎, ‎Iran

10.22108/ijgt.2017.21222

Abstract

‎‎For a finite group $G$‎, ‎let $\nu_{nc}(G)$ denote the number of conjugacy classes of non-normal non-cyclic subgroups of $G$‎. ‎We characterize the finite non-nilpotent groups whose all non-normal non-cyclic subgroups are conjugate‎.

Keywords

20.1001.1.22517650.2017.6.4.3.0

Main Subjects

20E45 Conjugacy classes

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