Title : Rank reduction of string C-groups
Speaker: Peter Brooksbank
Affiliation: Bucknell University
Time: 14:00 Tuesday, 26 February, 2019
Location: 303-257
Abstract
A string C-group is a group G together with a distinguished set of generating involutions satisfying certain conditions. These objects arise naturally as (and in fact are equivalent to) automorphism groups of abstract regular polytopes, which are generalizations of the familiar Platonic solids. Classifying the string C-group representations of a given family of groups is, by and large, an unrealistic aspiration. A more tractable goal is to determine the possible ranks of such representations, namely the number of generating involutions. I will discuss a technique that can be used to study this problem: given a string C-group of rank r, it attempts to build one of rank r-1. I will also present an elementary, easy to verify criterion that ensures success, and give some applications of rank reduction to familiar group families such as symmetric groups and classical groups.

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