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

‎‎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.

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Bibliographic Details
Published inInternational journal of group theory Vol. 6; no. 4; pp. 35 - 40
Main Authors Hamid Mousavi, Zahra Rezazadeh
Format Journal Article
LanguageEnglish
Published University of Isfahan 01.12.2017
Subjects
Conjugacy classes of non-normal subgroups
Non-nilpotent groups
Non-normal subgroups
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Summary:‎‎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.
ISSN:2251-7650
2251-7669
DOI:10.22108/ijgt.2017.21222