A note on locally graded minimal non-metahamiltonian groups

ATLIHAN S.

TURKISH JOURNAL OF MATHEMATICS, cilt.41, sa.5, ss.1140-1143, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 41 Sayı: 5
  • Basım Tarihi: 2017
  • Doi Numarası: 10.3906/mat-1503-31
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.1140-1143
  • Gazi Üniversitesi Adresli: Evet

Özet

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.