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Séminaire Géométrie et groupes discrets
# Equations in Periodic Groups

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Europe/Paris

Centre de conférences Marilyn et James Simons (IHES)
### Centre de conférences Marilyn et James Simons

#### IHES

Le Bois Marie
35, route de Chartres
91440 Bures-sur-Yvette

Description

- The free Burnside group B(r,n) is the quotient of the free group of rank r by the normal subgroup generated by the n-th power of all its elements. It was introduced in 1902 by Burnside, who asked whether B(r,n) is necessarily a finite group or not. In 1968 Novikov and Adian proved that if r > 1 and n is a sufficiently large odd exponent, then B(r,n) is actually infinite. It turns out that B(r,n) has a very rich structure. In this talk we are interested in understanding equations in B(r,n). In particular we want to investigate the following problem: given a set of equations S, under which conditions does every solution to S in B(r,n) already come from a solution in the free group of rank r?
- Along the way we will explore other aspects of certain periodic groups (i.e. quotients of a free Burnside group) such as the Hopf / co-Hopf property, the isomorphism problem, their automorphism groups, etc.
- Joint work with Z. Sela.

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__IHES Covid-19 regulations__:

- all the participants who will attend the event in person will have to keep their mask on in indoor spaces

and where the social distancing is not possible;

- speakers will be free to wear their mask or not at the moment of their talk if they feel more comfortable

without it;

- Up to 70 persons in the conference room, every participant will be asked to be able to provide a health pass

- Over 70 persons in the conference room, every participant will be asked to provide a health pass which will

be checked at the entrance of the conference room.

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Organized by

Fanny Kassel

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