Elliptic subgroups in cyclic splittings of a free group
Abstract
We use Gersten's generalization of Whitehead's algorithm to determine whether a given finitely generated subgroup of a free group F is elliptic in an elementary cyclic splitting of F. We provide a similar result for all elementary cyclic splittings of a free group of rank two and partial results towards an algorithm for ellipticity in elementary cyclic splittings of F as an HNN-extension.
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