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


Groups and Combinatorics Seminar, Semisymmetric graphs of prime valency 
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Abstract:
A graph is called Xsemisymmetric if the group X acts transitively on edges, but not on vertices. Such graphs are necessarily bipartite and biregular, 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 biregular 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 Xsemisymmetric (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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