On redundant Sylow subgroups

authored by

Benjamin Sambale

Abstract

A Sylow p-subgroup P of a finite group G is called redundant if every p-element of G lies in a Sylow subgroup different from P. Generalizing a recent theorem of Maróti–Martínez–Moretó, we show that for every non-cyclic p-group P there exists a solvable group G such that P is redundant in G. Moreover, we answer several open questions raised by Maróti–Martínez–Moretó.

Organisation(s)

Institute of Algebra, Number Theory and Discrete Mathematics

Type

Article

Journal

Journal of algebra

Volume

650

Pages

1-9

No. of pages

9

ISSN

0021-8693

Publication date

10.04.2024

Publication status

E-pub ahead of print

Peer reviewed

Yes

ASJC Scopus subject areas

Algebra and Number Theory

Electronic version(s)

https://doi.org/10.48550/arXiv.2311.06931 (Access: Open)
https://doi.org/10.1016/j.jalgebra.2024.04.002 (Access: Open)