Abstract

The length of a finite group G is defined to be the length of the longest chain in the subgroup lattice of G; this notion has been the subject of numerous papers dating back to the 1960s, especially in the context of simple groups. In recent joint work with Martin Liebeck and Aner Shalev, we introduce and study a related concept called the depth of G and it is interesting to compare these two parameters. In this talk, I will discuss some of the main ideas and we will look at a number of concrete examples. I'll also present some recent results on the length and depth of finite simple groups, as well as natural extensions of these notions to some interesting families of infinite groups, such as algebraic groups and Lie groups.