Archivo de la etiqueta: conjugacy class

Paper «On products of groups and indices not divisible by a given prime» published in Monatsh. Math.

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María José Felipe, Lev S. Kazarin, Ana Martínez-Pastor, and Víctor Sotomayor.
On products of groups and indices not divisible by a given prime.
Comm. Algebra, 193(4):811–827, 2020.

doi:10.1007/s00605-020-01446-z

Abstract

Let the group G = AB be the product of subgroups A and B, and let p be a prime. We prove that p does not divide the conjugacy class size (index) of each p-regular element of prime power order x ∈ A ∪ B if and only if G is p-decomposable, i.e. G=Op(G) × Op’(G).

2020 Mathematics Subject Classification: 20D40, 20E45, 20D20, 20D60

Keywords: Finite groups; products of groups; conjugacy classes; p-structure; prime graph; almost simple groups

Paper «On finite groups with square-free conjugacy class sizes» published in Int. J. Group Theory

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María José Felipe, Ana Martínez-Pastor, Víctor-Manuel Ortiz-Sotomayor

On finite groups with square-free conjugacy class sizes

Int. J. Group Th., 7 (2):17-24, 2018

doi:10.22108/ijgt.2017.21475

Abstract

We report on finite groups having square-free conjugacy class sizes, in particular in the framework of factorised groups.

2010 Mathematics Subject Classification: Primary: 20E45. Secondary: 20D40, 20D10, 20D20

Keywords: finite group, conjugacy class, factorised group