Bounding the number of classes of a finite group in terms of a prime-Reference-Cited by-同舟云学术

Bounding the number of classes of a finite group in terms of a prime

Author:

Maróti Attila¹,Simion Iulian I.²

Affiliation:

1. Hungarian Academy of Sciences, Alfréd Rényi Institute of Mathematics, Reáltanoda utca 13-15, H-1053, Budapest, Hungary

2. Department of Mathematics, “Babeş-Bolyai” University, str. Ploieşti nr.23-25, 400157Cluj-Napoca, Romania

Abstract

AbstractHéthelyi and Külshammer showed that the number of conjugacy classes

{k(G)}

of any solvable finite group G whose order is divisible by the square of a prime p is at least

{(49p+1)/60}

. Here an asymptotic generalization of this result is established. It is proved that there exists a constant

{c>0}

such that, for any finite group G whose order is divisible by the square of a prime p, we have

{k(G)\geq cp}

Funder

Horizon 2020 Framework Programme

Nemzeti Kutatási Fejlesztési és Innovációs Hivatal

Publisher

Walter de Gruyter GmbH

Subject

Algebra and Number Theory

Link

Reference42 articles.

3. On Loewy lengths of centers of blocks;Proceedings of the 49th Symposium on Ring Theory and Representation Theory,2017

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