RUS  ENG
Full version
JOURNALS // Sibirskii Matematicheskii Zhurnal // Archive

Sibirsk. Mat. Zh., 2012 Volume 53, Number 5, Pages 967–977 (Mi smj2322)

This article is cited in 7 papers

A note on groups in which the centralizer of every element of order $5$ is a $5$-group

S. Astilla, Ch. Parkerb, R. Waldeckerc

a Department of Mathematics, The University of Bristol, Bristol, United Kingdom
b School of Mathematics, University of Birmingham, Birmingham, United Kingdom
c Institut für Mathematik, Universität Halle-Wittenberg, Halle, Germany

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.

Keywords: finite group.

UDC: 512.54

Received: 22.03.2011


 English version:
Siberian Mathematical Journal, 2012, 53:5, 772–780

Bibliographic databases:


© Steklov Math. Inst. of RAS, 2024