Irreducible Characters with Cyclic Anchor Group-Reference-Cited by-同舟云学术

Irreducible Characters with Cyclic Anchor Group

Published:2023-10-06 Issue:10 Volume:12 Page:950
ISSN:2075-1680
Container-title:Axioms
language:en
Short-container-title:Axioms

Author:

Algreagri Manal H.¹²^ORCID,Alghamdi Ahmad M.¹^ORCID

Affiliation:

1. Department of Mathematical Sciences, Faculty of Applied Sciences, Umm Al-Qura University, P.O. Box 14035, Makkah 21955, Saudi Arabia

2. Department of Mathematics, Jamoum University College, Umm Al-Qura University, P.O. Box 14035, Makkah 21955, Saudi Arabia

Abstract

We consider G to be a finite group and p as a prime number. We fix ψ to be an irreducible character of G with its restriction to all p-regular elements of G and ψ0 to be an irreducible Brauer character. The main aim of this paper is to describe and investigate the relationship between cyclic anchor group of ψ and the defect group of a p-block which contains ψ. Our methods are to study and generalize some facts for the cyclic defect groups of a p-block B to the case of a cyclic anchor group of irreducible characters which belong to B. We establish and prove a criteria for an irreducible character to have a cyclic anchor group.

Publisher

MDPI AG

Subject

Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis

Link

https://www.mdpi.com/2075-1680/12/10/950/pdf

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