FINITE SOLVABLE TIDY GROUPS ARE DETERMINED BY HALL SUBGROUPS WITH TWO PRIMES

FINITE SOLVABLE TIDY GROUPS ARE DETERMINED BY HALL SUBGROUPS WITH TWO PRIMES

In this paper, we investigate finite solvable tidy groups. We prove that a solvable group with order divisible by at least two primes is tidy if all of its Hall subgroups that are divisible by only two primes are tidy.

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Veröffentlicht in:Bulletin of the Australian Mathematical Society 2024-04, Vol.109 (2), p.342-349
Hauptverfasser: BEIKE, NICOLAS F., CARLETON, RACHEL, COSTANZO, DAVID G., HEATH, COLIN, LEWIS, MARK L., LU, KAIWEN, PEARCE, JAMIE D.
Format: Artikel
Sprache:eng
Schlagworte:
Hypotheses
Subgroups
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Zusammenfassung:In this paper, we investigate finite solvable tidy groups. We prove that a solvable group with order divisible by at least two primes is tidy if all of its Hall subgroups that are divisible by only two primes are tidy.
ISSN:0004-9727
1755-1633
DOI:10.1017/S0004972723000710