SEMINAR: Groups and Combinatorics Seminar, Semisymmetric graphs of prime valency
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Groups and Combinatorics Seminar, Semisymmetric graphs of prime valency |
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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)
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Location |
Weatherburn Lecture Theatre
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Contact |
Irene Pivotto
<[email protected]>
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Start |
Fri, 09 Aug 2013 15:00
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End |
Fri, 09 Aug 2013 16:00
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Submitted by |
Irene Pivotto <[email protected]>
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Last Updated |
Wed, 02 Oct 2013 16:08
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