Counting Centralizers in Finite Groups

belcastro, sarah-marie; Sherman, Gary J.

doi:10.2307/2690998

Cited by 41 publications

(50 citation statements)

References 8 publications

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“…We say that a group G (not necessarily finite group) has n centralizers (or G is a C n -group) if |cent(G)| = n. It is clear that a group is a C 1 -group if and only if it is abelian. The class of finite C n -groups was introduced by Belcastro and Sherman in [3] and investigated by many authors. For instance, see [5,8] for finite C n -groups and [11] for infinite C n -groups.…”

Section: Introductionmentioning

confidence: 99%

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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Section: Introductionmentioning

confidence: 99%

Groups with the same number of centralizers

Khoramshahi

Zarrin

2020

J. Algebra Appl.

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“…It is clear that a group G is a C 1 -group if and only if it is abelian. Belcastro and Sherman in [1], showed that there is no finite C n -group for n ∈ {2, 3}. Also they characterized all finite C n -groups for n ∈ {4, 5}.…”

Section: Introduction and Resultsmentioning

confidence: 99%

Criteria for the solubility of finite groups by their centralizers

Zarrin

2011

Arch. Math.

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“…We denote by Cent(G) = {C G (g) | g ∈ G}, where C G (g) is the centralizer of an element g ∈ G. A group G is called n-centralizer if |Cent(G)| = n. It is clear that a group is 1-centralizer if and only if it is abelian. Belcastro and Sherman proved the following results in [7]:…”

Section: Introduction and Resultsmentioning

confidence: 99%