Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5771678 | Journal of Algebra | 2018 | 11 Pages |
Abstract
Let p be a prime. Let A be a finite group and M be a normal subgroup of A such that all elements in AâM have order p. Suppose that A acts on a finite pâ²-group G in such a way that CG(M)=1. We show that if CG(x) is nilpotent for any xâAâM, then G is nilpotent. It is also proved that if A is a p-group and CG(x) is nilpotent of class at most c for any xâAâM, then the nilpotency class of G is bounded solely in terms of c and |A|.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Emerson de Melo, Jhone Caldeira,