# ALGEBRAIC COMBINATORICS

Skew product groups for monolithic groups
Algebraic Combinatorics, Volume 5 (2022) no. 5, pp. 785-802.

Skew morphisms, which generalise automorphisms for groups, provide a fundamental tool for the study of regular Cayley maps and, more generally, for finite groups with a complementary factorisation $G=BY$, where $Y$ is cyclic and core-free in $G$. In this paper, we classify all examples in which $B$ is monolithic (meaning that it has a unique minimal normal subgroup, and that subgroup is not abelian) and core-free in $G$. As a consequence, we obtain a classification of all proper skew morphisms of finite non-abelian simple groups.

Revised:
Accepted:
Published online:
DOI: 10.5802/alco.206
Classification: 20D99,  05E18,  05C25
Keywords: skew morphisms, regular Cayley maps, group factorisation
Bachratý, Martin 1; Conder, Marston 2; Verret, Gabriel 2

1 Mathematics Department Slovak University of Technology 81005 Bratislava Slovakia
2 Mathematics Department University of Auckland PB 92019 Auckland New Zealand
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Bachratý, Martin; Conder, Marston; Verret, Gabriel. Skew product groups for monolithic groups. Algebraic Combinatorics, Volume 5 (2022) no. 5, pp. 785-802. doi : 10.5802/alco.206. https://alco.centre-mersenne.org/articles/10.5802/alco.206/

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