On element-centralizers in finite groups.

DOI10.1007/s00013-009-0060-1zbMath1187.20016OpenAlexW2029338643MaRDI QIDQ1047897

Mohammad Zarrin

Publication date: 8 January 2010

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00013-009-0060-1

zbMATH Keywords

finite groupsminimal simple groupsnumbers of centralizers

Mathematics Subject Classification ID

Arithmetic and combinatorial problems involving abstract finite groups (20D60) Special subgroups (Frattini, Fitting, etc.) (20D25) Simple groups: alternating groups and groups of Lie type (20D06)

Related Items (24)

Centralizers in a group whose central factor is simple ⋮ Characterizations of some groups in terms of centralizers ⋮ Counting centralizers and z-classes of some F-groups ⋮ On finite groups with nine centralizers ⋮ On groups with same number of centralizers ⋮ Groups in which the centralizer of any non-central element is maximal ⋮ On capable groups of order p2q ⋮ On F-groups with the central factor of order p ⁴ ⋮ Counting the number of centralizers of 2-element subsets in a finite group ⋮ A characterization of 4-centralizer groups. ⋮ Groups with exactly ten centralizers ⋮ Finite groups with a given number of relative centralizers ⋮ Acentralizers of Abelian groups of rank 2 ⋮ On 10-centralizer groups of odd order. ⋮ ON NONCOMMUTING SETS AND CENTRALISERS IN INFINITE GROUPS ⋮ A generalization of Neumann's question ⋮ On the centralizers of the \(p\)-regular elements in a finite group ⋮ Finite groups determined by the number of element centralizers ⋮ Lie algebras with few centralizers ⋮ On the set of same-size conjugate classes ⋮ Groups with the same number of centralizers ⋮ On 9-centralizer groups ⋮ On Finite n-Acentralizer Groups ⋮ Derived length and centralizers of groups

Uses Software

• GAP

Cites Work

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• Insoluble groups with the rewriting property \(P_ 8\)
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• Non-commuting graph of a group.
• FINITE AXIOMATIZATION OF FINITE SOLUBLE GROUPS
• On Finite Groups with a Given Number of Centralizers
• Counting Centralizers in Finite Groups
• Nonsolvable finite groups all of whose local subgroups are solvable
• Endliche Gruppen I

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