** "Geometry and Analysis on Groups" Research Seminar **

**Time:** 15:00–17:00

**Location:** Seminarraum 9, Oskar-Morgenstern-Platz 1, 2.Stock

**Title:** Maximal subgroups of groups of intermediate growth.

**Speaker:** Alejandra Garrido (Düsseldorf).

**Abstract:**The index and number of maximal subgroups of a (countable group) is a measure of the group's size and complexity. There is a rough correlation between this notion of size and another usual notion of size of a finitely generated group, word growth. Namely, groups of polynomial growth have all maximal subgroups of finite index (and therefore countably many them), while those of exponential growth tend to have uncountably many maximal subgroups of infinite index.
I will discuss some joint work with D. Francoeur (Geneva) on the maximal subgroups of some groups of intermediate growth which arise as non-torsion generalizations of the first Grigorchuk group.