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SUMMARY:The soluble graph of a finite group - Tim Burness (University of B
 ristol)
DTSTART:20220705T101500Z
DTEND:20220705T111500Z
UID:TALK175634@talks.cam.ac.uk
DESCRIPTION:Let G be a finite insoluble group with soluble radical R(G). T
 he vertices of the soluble graph of G\, denoted Gamma_S(G)\, are labelled 
 by the elements in G\\R(G)\, with x and y adjacent if they generate a solu
 ble subgroup of G. This is a natural generalisation of the widely studied 
 commuting graph of G.\n&nbsp\;\nIn this talk I will report on joint work w
 ith Andrea Lucchini and Daniele Nemmi\, which establishes several new resu
 lts on Gamma_S(G). Our main theorem states that this graph is always conne
 cted\, with diameter at most 5. We can construct examples with diameter 4\
 , so our upper bound on the diameter is close to best possible. I will exp
 lain some of the main ideas and I will present a number of open problems.
LOCATION:Seminar Room 2\, Newton Institute
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