Conference abstracts

Session S12 - Group Theory

July 29, 17:30 ~ 18:20

## Connectedness of generating sets for finite groups

### Marston Conder

### University of Auckland, Nueva Zelanda - m.conder@auckland.ac.nz

Suppose $G$ is a finitely-generated group, and $X$ and $Y$ are two generating sets for $G$ with $|X| = |Y|$. Under what conditions can $X$ be `transformed' to $Y$ by a sequence of single-element replacements? This very general question relates to a number of things, including the product replacement algorithm, T-systems for finite groups, and expansion in Cayley graphs. Some recent progress will be described, especially in the case of 2-generator finite groups.