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SEMINAR: Groups and Combinatorics Seminar, Semisymmetric graphs of prime valency

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Today's date is Tuesday, October 20, 2020
Groups and Combinatorics Seminar, Semisymmetric graphs of prime valency Other events...
Abstract:

A graph is called X-semisymmetric if the group X acts transitively on edges, but not on vertices. Such graphs are necessarily bipartite and bi-regular, of valencies k and l say. There is a natural relationship between semisymmetric graphs and amalgams of groups. This leads us to consider the "universal" example: the bi-regular tree T of valencies k and l. The conjecture of Goldschmidt says that when k and l are primes there are (up to isomorphism) finitely many locally finite groups X such that T is X-semisymmetric (X is locally finite if it acts with finite vertex stabilisers). For k=l=3 it was shown by Goldschmidt that there are 15 such groups. In the talk I will give an overview of some results which bear relevance to the conjecture, and report on some recent progress with respect to certain small primes.
Speaker(s) Luke Morgan (UWA)
Location Weatherburn Lecture Theatre
Contact Irene Pivotto <[email protected]>
Start Fri, 09 Aug 2013 15:00
End Fri, 09 Aug 2013 16:00
Submitted by Irene Pivotto <[email protected]>
Last Updated Wed, 02 Oct 2013 16:08
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