Algebraic Graph Theory Seminar - Martin Bachratý (24.4.2026)
Friday 24.4.2026 at 13:15, Lecture room M IX (online too)
Martin Bachratý (Slovak University of Technology, Bratislava):
Skew morphisms of cyclic 2-groups
Abstract:
Skew morphisms are permutations of finite groups that generalise group automorphisms, and they lie at the intersection of map theory and group factorizations. The classification and enumeration of skew morphisms for various families of finite groups is a central problem in the area, and has been carried out for several notable families, including simple groups, dihedral groups, and cyclic p-groups with p odd. The case of cyclic 2-groups has resisted the same treatment — until now. After explaining the connections between Cayley maps, group factorizations, and skew morphisms, we present a complete enumeration of skew morphisms of cyclic 2-groups, completing the enumeration for all cyclic p-groups by treating the remaining case p=2.
The speaker acknowledges funding from the EU NextGenerationEU through the Recovery and Resilience Plan for Slovakia under the project No. 09I03-03-V04-00272.