The structure of finite groups with three class sizes
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Título
The structure of finite groups with three class sizesFecha de publicación
2009Editor
Walter de GruyterISSN
1433-5883Tipo de documento
info:eu-repo/semantics/articleVersión de la editorial
https://www.degruyter.com/document/doi/10.1515/JGT.2008.095/htmlVersión
info:eu-repo/semantics/publishedVersionPalabras clave / Materias
Resumen
Let G be a finite group and suppose that the set of conjugacy class sizes of G is f1; m; mng, where m; n > 1 are coprime. We prove that m 1⁄4 p for some prime p dividing n 1. We also show that G has an abelian ... [+]
Let G be a finite group and suppose that the set of conjugacy class sizes of G is f1; m; mng, where m; n > 1 are coprime. We prove that m 1⁄4 p for some prime p dividing n 1. We also show that G has an abelian normal p-complement and that if P is a Sylow p-subgroup of G, then jP0j 1⁄4 p and jP=ZðGÞpj 1⁄4 p2. We obtain other properties and deter- mine completely the structure of G. [-]
Publicado en
Journal of Group Theory, vol. 12 (2009), p. 539–553Derechos de acceso
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- MAT_Articles [770]