Seminár z algebraickej teórie grafov - Martin Bachratý (28.3.2025)

v piatok 28.3.2025 o 13:15 hod. v posluchárni M IX aj online

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Prednášajúci: Martin Bachratý, Slovak University of Technology, Bratislava
(joint work with Michal Hagara)

Názov: Recursive characterisation of skew morphisms of finite cyclic groups

Termín: 28.3.2025, 13:15 hod., M IX a MS Teams 

Abstrakt:
A skew morphism of a finite group G is a specific permutation of G, the definition of which closely resembles that of a group automorphism. Skew morphisms were first introduced in the paper by Robert Jajcay and Jozef Širáň in 2002, where it was shown that they are closely related to regular Cayley maps. One of the most prominent problems about skew morphisms is to find their classification for all finite cyclic groups. Despite substantial progress over the last decade this problem still remains open. In this talk, we explore different ways in which a skew morphism of a cyclic group can be reduced to a smaller skew morphism, as well as possible methods for reconstructing a skew morphism from its reductions. In particular, we show that each skew morphism of the cyclic group of order n is uniquely determined by two suitable reductions and one element of the group. This leads to a recursive characterisation of skew morphisms for all finite cyclic groups.

The speaker acknowledges funding from the EU NextGenerationEU through the Recovery and Resilience Plan for Slovakia under the project No. 09I03-03-V04-00272.

 

Those of you who are not able to attend in person or who are still uncertain about the safety of attending in person are welcome to attend via MS Teams. In either case, we hope to see as many of you as possible (either in person or virtually) at our Friday gatherings.

 

 

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