#### Atılım University General Seminars

Implications of the index of a fixed point subgroups
Erkan Murat Türkan
Çankaya University, Turkey
Özet : Let G be a finite group and A be a subgroup of the automorphism group Aut(G) of G. In this work, we studied the influence of the index of fixed point subgroup of A in G on the structure of G. When A is cyclic, we proved the following: (1) [G, A] is solvable if this index is squarefree and the orders of G and A are coprime. (2) G is solvable if the index of the centralizer of each x in H−G is squarefree where H denotes the semidirect product of G by A.
 Tarih : 08.05.2019 Saat : 15:40 Yer : FEF 404 Dil : English