Murray Elder
Friday 2nd September, 12.0512.55pm, Carslaw 275
Looking for short words in the first Grigorchuk group
The "first" Grigorchuk group as it is known is a finitely
generated group that is not finitely presented, although it does have
a nice recursive definition. Every element has finite order but it is
infinite, and its growth function f(n), which counts the number of
elements represented by a word of length n with respect to some
generating set, is between polynomial and exponential. Grigorchuk came
up with this group in the 80s, answering a question of Milnor as to
whether any group could have "intermediate" growth.
In my talk I will explain this group and discuss our current work to
describe the set of all "geodesic" or shortest length words with
respect to a four generator generating set. This set has some
intriguing structure, for instance, it contains an indexed language
such that no infinite subset is contextfree.
The talk will require no background knowledge much, except for knowing
what a group presentation is. This is joint work with Mauricio
Gutierrez and Zoran Sunik.
