Skew product groups for monolithic groups
Algebraic Combinatorics, Tome 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.

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DOI : 10.5802/alco.206
Classification : 20D99, 05E18, 05C25
Mots clés : 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, Tome 5 (2022) no. 5, pp. 785-802. doi : 10.5802/alco.206. http://www.numdam.org/articles/10.5802/alco.206/

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