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Seminar: Verbally closed subgroups of free groups (E. Ventura, UPC)

Date: Friday April 12th, 12-13
Place: CRM, room A2
Títle: Verbally closed subgroups of free groups.
Speaker: Enric Ventura, UPC

Abstract: This talk will be an exposition of the results contained in the recent preprint "Verbally closed subgroups of free groups" by A. Myasnikov and V. Roman'kov. The main result is: a f.g. subgroup H of a f.g. free group is algebraically closed if and only if it is verbally closed, and if and only if it is a retract (precise definitions will be discussed). As a consequence, a notion of "verbal closure" of H will make sense, it will be finitely generated again, and effectively computable from given generators for H. This result is a nice connection between a model theoretic concept (algebraically closed subgroups) and an algebraic one (retracts), passing through the intermediate notion of verbally closed subgroups (also classical in the literature). Altogether taking also care of the corresponding algorithmic issues, and with easy proofs and arguments.

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