TY - JOUR

T1 - On redundant Sylow subgroups

AU - Sambale, Benjamin

PY - 2024/4/10

Y1 - 2024/4/10

N2 - 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.

AB - 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.

KW - Covering p-elements

KW - Sylow subgroups

UR - http://www.scopus.com/inward/record.url?scp=85190160171&partnerID=8YFLogxK

U2 - 10.48550/arXiv.2311.06931

DO - 10.48550/arXiv.2311.06931

M3 - Article

AN - SCOPUS:85190160171

VL - 650

SP - 1

EP - 9

JO - Journal of algebra

JF - Journal of algebra

SN - 0021-8693

ER -