1. A GENERALIZED FIXED-POINT-FREE ACTION.
- Author
-
GÜLOĞLU, İSMAİL Ş. and ERCAN, GÜLİN
- Subjects
- *
GENERALIZATION , *FIXED point theory , *FINITE groups , *AUTOMORPHISMS , *PROBLEM solving , *NILPOTENT groups , *ABELIAN groups - Abstract
In this paper we study the structure of a finite group G admitting a solvable group A of automorphisms of coprime order so that for any x ∈ CG(A) of prime order or of order 4, every conjugate of x in G is also contained in CG(A). Under this hypothesis it is proven that the subgroup [G, A] is solvable. Also an upper bound for the nilpotent height of [G, A] in terms of the number of primes dividing the order of A is obtained in the case where A is abelian. [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
- View/download PDF