Mathematics – Group Theory
Scientific paper
2009-06-21
Mathematics
Group Theory
65 pages, 12 figures. This submission replaces the paper Effective Grushko Decompositions, the previous version contains a gap
Scientific paper
We present an algorithm which given a presentation of a group G without 2-torsion, a solution to the word problem with respect to this presentation, and an acylindricity constant {\kappa}, outputs a collection of tracks in an appropriate presentation complex. We give two applications: the first is an algorithm which decides if G admits an essential free decomposition, the second is an algorithm which; if G is relatively hyperbolic; decides if it admits an essential elementary splitting.
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