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 , where is cyclic and core-free in . In this paper, we classify all examples in which is monolithic (meaning that it has a unique minimal normal subgroup, and that subgroup is not abelian) and core-free in . As a consequence, we obtain a classification of all proper skew morphisms of finite non-abelian simple groups.
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Mots clés : skew morphisms, regular Cayley maps, group factorisation
@article{ALCO_2022__5_5_785_0,
author = {Bachrat\'y, Martin and Conder, Marston and Verret, Gabriel},
title = {Skew product groups for monolithic groups},
journal = {Algebraic Combinatorics},
pages = {785--802},
publisher = {The Combinatorics Consortium},
volume = {5},
number = {5},
year = {2022},
doi = {10.5802/alco.206},
language = {en},
url = {http://www.numdam.org/articles/10.5802/alco.206/}
}
TY - JOUR AU - Bachratý, Martin AU - Conder, Marston AU - Verret, Gabriel TI - Skew product groups for monolithic groups JO - Algebraic Combinatorics PY - 2022 SP - 785 EP - 802 VL - 5 IS - 5 PB - The Combinatorics Consortium UR - http://www.numdam.org/articles/10.5802/alco.206/ DO - 10.5802/alco.206 LA - en ID - ALCO_2022__5_5_785_0 ER -
%0 Journal Article %A Bachratý, Martin %A Conder, Marston %A Verret, Gabriel %T Skew product groups for monolithic groups %J Algebraic Combinatorics %D 2022 %P 785-802 %V 5 %N 5 %I The Combinatorics Consortium %U http://www.numdam.org/articles/10.5802/alco.206/ %R 10.5802/alco.206 %G en %F ALCO_2022__5_5_785_0
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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