On Minimal Non-Soluble Groups, the Normalizer Condition and McLain Groups


ARIKAN A.

ADVANCES IN GROUP THEORY AND APPLICATIONS, cilt.3, ss.1-12, 2017 (ESCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 3
  • Basım Tarihi: 2017
  • Doi Numarası: 10.4399/97888255036921
  • Dergi Adı: ADVANCES IN GROUP THEORY AND APPLICATIONS
  • Sayfa Sayıları: ss.1-12

Özet

We prove that a minimal non-soluble (MNS in short) Fitting p-group G has a proper subgroup K such that for every proper subgroup R of G containing K, we have N-G (R) > R. In other words, G satisfies the normalizer condition modulo K. We also give a positive answer in McLain groups to a question aroused from the works on MNS Fitting p-groups.