Groups in which the centralizer of any non-central element is maximal-Reference-Cited by-同舟云学术

Groups in which the centralizer of any non-central element is maximal

Published:2020-03-10 Issue:5 Volume:23 Page:871-878
ISSN:1435-4446
Container-title:Journal of Group Theory
language:en
Short-container-title:

Author:

Zhao Xianhe¹,Chen Ruifang²,Guo Xiuyun³

Affiliation:

1. College of Mathematics and Information Science, Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control , Henan Normal University , Xinxiang Henan 453007 , P. R. China

2. College of Mathematics and Information Science , Henan Normal University , Xinxiang Henan 453007 , P. R. China

3. Department of Mathematics , Shanghai University , Shanghai 200444 , P. R. China

Abstract

Abstract Let x be an element of a finite group G. It is clear that 〈 x 〉 ≤ C G ⁢ ( x ) ≤ G

{\langle x\rangle\leq C_{G}(x)\leq G}

. For the cases where C G ⁢ ( x ) = G

{C_{G}(x)=G}

and C G ⁢ ( x ) = 〈 x 〉

{C_{G}(x)=\langle x\rangle}

for any element x of G, the structure of G is easily decided. In this paper, we investigate the case where C G ⁢ ( x )

{C_{G}(x)}

is maximal in G and obtain the structure of G.

Funder

National Natural Science Foundation of China

Henan Normal University

Publisher

Walter de Gruyter GmbH

Subject

Algebra and Number Theory

Reference13 articles.

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