Action of a Frobenius-like group with kernel having central derived subgroup
INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, cilt.26, ss.1257-1265, 2016 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 26
- Basım Tarihi: 2016
- Doi Numarası: 10.1142/s0218196716500533
- Dergi Adı: INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.1257-1265
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Orta Doğu Teknik Üniversitesi Adresli: Evet
Özet
A finite group FH is said to be Frobenius-like if it has a nontrivial nilpotent normal subgroup F with a nontrivial complement H such that [F, h] = F for all nonidentity elements h is an element of H. Suppose that a finite group G admits a Frobenius-like group of auto-morphisms FH of coprime order with [F', H] = 1. In case where C-G( F) = 1 we prove that the groups G and C-G( H) have the same nilpotent length under certain additional assumptions.