On redundant Sylow subgroups

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...

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Bibliographic Details
Published in:Journal of algebra 2024-07, Vol.650, p.1-9
Main Author: Sambale, Benjamin
Format: Article
Language:English
Subjects:
Covering p-elements
Sylow subgroups
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Summary: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.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2024.04.002