Algebraic Graph Theory Seminar - Martin Bachratý (12.11.2021)

Friday 12.11.2021 at 13:00, Lecture room M X or online

11. 11. 2021 09.07 hod.
By: Martin Mačaj

Martin Bachratý (Slovak University of Technology):
Skew morphisms for cyclic groups of small order

MS Teams (AGT in Bratislava team, scheduled meeting)

Abstract:
A skew morphism of a finite group *B* is a permutation φ of *B* preserving the identity element of *B* and having the property that for every *a* ∈ *B* there exists a positive integer *j(a) *satisfying φ(*ab*) = φ(*a*)φ*ʲ⁽ᵃ⁾*(*b*) for all *b* ∈ *B. *In this talk I will explain how skew morphisms naturally arise from the study of regular Cayley maps. I will also outline what is known about skew morphisms of cyclic groups, and how this can be used to find all skew morphisms for cyclic groups of order up to 161.

Thanks to (temporary?) loosening of restrictions regarding the COVID epidemy, we intend to conduct the seminar meetings this semester `in-person'. Hence, all of you who might choose to attend in person are welcome. 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.