Square-free class sizes in products of groups

Square-free class sizes in products of groups

We obtain some structural properties of a factorised group \(G = AB\), given that the conjugacy class sizes of certain elements in \(A\cup B\) are not divisible by \(p^2\), for some prime \(p\). The case when \(G = AB\) is a mutually permutable product is especially considered.

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Veröffentlicht in:arXiv.org 2017-03
Hauptverfasser: Felipe, M J, Martínez-Pastor, A, Ortiz-Sotomayor, V M
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics - Group Theory
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Zusammenfassung:We obtain some structural properties of a factorised group \(G = AB\), given that the conjugacy class sizes of certain elements in \(A\cup B\) are not divisible by \(p^2\), for some prime \(p\). The case when \(G = AB\) is a mutually permutable product is especially considered.
ISSN:2331-8422
DOI:10.48550/arxiv.1703.08363