Isoperimetric Functions of Groups and Computational Complexity of the Word Problem

Details Isoperimetric Functions of Groups and Computational Complexity of the Word Problem Isoperimetric Functions of Groups and Computational Complexity of the Word Problem

1998-11-18

arxiv.org/abs/math/9811106v1

Mathematics

Group Theory

47 pages

Scientific paper

We prove that the word problem of a finitely generated group $G$ is in NP
(solvable in polynomial time by a non-deterministic Turing machine) if and only
if this group is a subgroup of a finitely presented group $H$ with polynomial
isoperimetric function. The embedding can be chosen in such a way that $G$ has
bounded distortion in $H$.

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