학술논문
A note on groups in which the centralizer of every element of order 5 is a 5-group.
Document Type
Article
Author
Source
Subject
*GROUP theory
*TOPOLOGICAL degree
*FIXED point theory
*FINITE groups
*MATHEMATICAL analysis
*PRIME numbers
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Language
ISSN
0037-4466
Abstract
The main theorem in this article shows that a group of odd order which admits the alternating group of degree 5 with an element of order 5 acting fixed point freely is nilpotent of class at most 2. For all odd primes r, other than 5, we give a class 2 r-group which admits the alternating group of degree 5 in such a way. This theorem corrects an earlier result which asserts that such class 2 groups do not exist. The result allows us to state a theorem giving precise information about groups in which the centralizer of every element of order 5 is a 5-group. [ABSTRACT FROM AUTHOR]