• 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