Title of article
Characterization of finite groups with a unique non-nilpotent proper subgroup
Author/Authors
Taeri, Bijan Department of Mathematical Sciences - Isfahan University of Technology , Tayanloo-Beyg, Fatemeh Department of Mathematical Sciences - Isfahan University of Technology
Pages
7
From page
47
To page
53
Abstract
We characterize finite non-nilpotent groups G with a unique non-nilpotent proper subgroup. We show that |G| has at most three prime divisors. When G is supersolvable we find the presentation of G and when G is non-supersolvable we show that either G is a direct product of an Schmidt group and a cyclic group or a semi direct product of a p-group by a cyclic group of prime power order.
Keywords
Keywords
Finite groups , minimal non-abelian groups , minimal non-nilpotent groups , critical groups
Journal title
International Journal of Group Theory
Serial Year
2021
Record number
2526092
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