Charlotte Scott Centre for Algebra
School of Engineering and Physical Sciences, University of Lincoln
Algebra Research Seminar: Talk by Dr Martyn Quick (St Andrews)
Dr Martyn Quick (University of St Andrews, Scotland) is currently visiting the Charlotte Scott Research Centre for Algebra, to discuss maths with Lincoln algebraist Dr Simon Smith.
On 13 November 2024 Dr Quick spoke in our Algebra Seminar about his recent work on maximal subgroups of Thompson’s group V, reporting on recent developments from his collaborations with Jim Belk, Collin Bleak and Rachel Skipper. Title of the talk: Type systems and maximal subgroups in Thompson’s group VAbstract:
Thompson’s group V is a finitely presented infinite simple group that has been much studied since its introduction in 1965. It is most naturally described as a group of homeomorphisms of Cantor space given by piecewise prefix substitution maps. I will describe the concept of a type system, which is a partition of the set of finite words over the alphabet {0,1} that is compatible with the partial action of the group V on the basic clopen subsets of Cantor space, and how the stabilizers of certain simple type systems (including of all finite simple type systems) are maximal subgroups of V. In particular, this technology can be used to describe a new uncountable family of pairwise non-isomorphic maximal subgroups of V. (This is joint work with Belk, Bleak & Skipper.)
About Yuri Santos
Charlotte Scott Centre for Algebra 