On element-centralizers in finite groups

Zarrin, Mohammad

doi:10.1007/s00013-009-0060-1

Cited by 33 publications

(19 citation statements)

References 11 publications

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“…In this case, according to Lemma 3.21 of [1], one can obtain that the number of abelian centralizers of G is q 2 + q + 1. Therefore, by Case (2) of Theorem 1.1 of [7], we have…”

Section: Counterexample To Question 11mentioning

confidence: 91%

Groups with the same number of centralizers

Khoramshahi

Zarrin

2020

J. Algebra Appl.

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For any group [Formula: see text], let [Formula: see text] denote the set of all non-abelian centralizers of [Formula: see text]. Jafarian Amiri and Rostami, Groups with a few nonabelian centralizers, Publ. Math. Debrecen 87(3–4) (2015) 429–437 put forward the following question: Let [Formula: see text] and [Formula: see text] be finite simple groups. Is it true that if [Formula: see text], then [Formula: see text] is isomorphic to [Formula: see text]? In this paper, among other things, we give a negative answer to this question.

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“…In this case, according to Lemma 3.21 of [1], one can obtain that the number of abelian centralizers of G is q 2 + q + 1. Therefore, by Case (2) of Theorem 1.1 of [7], we have…”

Section: Counterexample To Question 11mentioning

confidence: 91%

Groups with the same number of centralizers

Khoramshahi

Zarrin

2020

J. Algebra Appl.

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“…It is clear that a group is a C 1 -group if and only if it is abelian. The class of C ngroups was introduced by Belcastro and Sherman in [7] and investigated by many authors (see, for example, [1,3,4,13,14,16]).…”

Section: Groups With a Finite Number Of Centralisersmentioning

confidence: 99%

On Noncommuting Sets and Centralisers in Infinite Groups

Zarrin¹

2015

Bull. Aust. Math. Soc.

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A subset $X$ of a group $G$ is a set of pairwise noncommuting elements if $ab\neq ba$ for any two distinct elements $a$ and $b$ in $X$. If $|X|\geq |Y|$ for any other set of pairwise noncommuting elements $Y$ in $G$, then $X$ is called a maximal subset of pairwise noncommuting elements and the cardinality of such a subset (if it exists) is denoted by ${\it\omega}(G)$. In this paper, among other things, we prove that, for each positive integer $n$, there are only finitely many groups $G$, up to isoclinism, with ${\it\omega}(G)=n$, and we obtain similar results for groups with exactly $n$ centralisers.

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“…A group is a -group if ( ) is abelian for every ∈ \ ( ). Many authors have studied the influence of |Cent( )| on finite group (see [1][2][3][4][5][6][7][8][9]). It is clear that a group is 1-centralizer if and only if it is abelian.…”

Section: Introductionmentioning

confidence: 99%