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

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Atıf İçin Kopyala

ARIKAN A.

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

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 3
• Basım Tarihi: 2017
• Doi Numarası: 10.4399/97888255036921
• Dergi Adı: ADVANCES IN GROUP THEORY AND APPLICATIONS
• Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
• Sayfa Sayıları: ss.1-12
• Gazi Üniversitesi Adresli: Evet

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.