A note on locally graded minimal non-metahamiltonian groups


ATLIHAN S.

TURKISH JOURNAL OF MATHEMATICS, vol.41, no.5, pp.1140-1143, 2017 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 41 Issue: 5
  • Publication Date: 2017
  • Doi Number: 10.3906/mat-1503-31
  • Title of Journal : TURKISH JOURNAL OF MATHEMATICS
  • Page Numbers: pp.1140-1143

Abstract

We prove that a nonperfect locally graded minimal non-metahamiltonian group G is a soluble group with derived length of at most 4. On the other hand, if G is perfect, then G/Phi(G) is isomorphic to A(5) , where Phi(G) is the Frattini subgroup of G and A(5) is the alternating group. Moreover, we show that under some conditions, if G is a p-group, then G is metabelian, where p is a prime integer.