Recognizing simple projective linear groups PSL(p; q) by their order and one conjugacy class length

Let r = (q^p−1)/(q−1)(p,q−1) be a prime number, where q is a prime power and p is an odd prime. In this paper, we will show that G = PSL(p; q) if and only if jGj = jPSL(p; q)j and G has a conjugacy class of size jGL( (qp-p;q 1))j.

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Publication Details

Journal
Boletim da Sociedade Paranaense de Matemática
Published
2025-03-24
DOI
https://doi.org/10.5269/bspm.70220
Primary Topic
Finite Group Theory Research
Type
article
Field-Weighted Citation Impact
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article

Recognizing simple projective linear groups PSL(p; q) by their order and one conjugacy class length

Alireza Khalili Asboei, Amirmohammad Momei Kohestani
Boletim da Sociedade Paranaense de Matemática
Finite Group Theory Research
article

Recognizing simple projective linear groups PSL(p; q) by their order and one conjugacy class length

Alireza Khalili Asboei, Amirmohammad Momei Kohestani
article en

Abstract

Let r = (q^p−1)/(q−1)(p,q−1) be a prime number, where q is a prime power and p is an odd prime. In this paper, we will show that G = PSL(p; q) if and only if jGj = jPSL(p; q)j and G has a conjugacy class of size jGL( (qp-p;q 1))j.

Boletim da Sociedade Paranaense de MatemáticaVol. 43
University of Mazandaran (IR), Farhangian University (IR)
Openalex Percentile: Top 76%
Finite Group Theory Research
DOIOpen Access PDFOpenAlex
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Recognizing simple projective linear groups PSL(p; q) by their order and one conjugacy class length — Alireza Khalili Asboei, Amirmohammad Momei Kohestani · Boletim da Sociedade Paranaense de Matemática (2025) | TGRS Research Map | TGRS