On the nilpotent length of a finite group with a Frobenius group of automorphisms

---

Tezin Türü: Doktora

Tezin Yürütüldüğü Kurum: Orta Doğu Teknik Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, Türkiye

Tezin Onay Tarihi: 2013

Öğrenci: ELİF ÖĞÜT

Danışman: GÜLİN ERCAN

Özet:

Let G be a finite group admitting a Frobenius group FH of automorphisms with kernel F and complement H. Assume that the order of G and FH are relatively prime and H acts regularly on the fixed point subgroup of F in G. It is proved in this thesis that the nilpotent length of G is less than or equal to the sum of the nilpotent length of the commutator group of G and F with 1 and the nilpotent length of the commutator group of G and F is equal to the nilpotent length of the fixed point subgroup of H in the commutator group of G and F.