# Isoperimetric functions of groups and computational complexity of the word problem

@article{JCBirget1998IsoperimetricFO, title={Isoperimetric functions of groups and computational complexity of the word problem}, author={J.-C.Birget and Alexander Yu. Olshanskii and Eliyahu Rips and M.Sapir}, journal={Annals of Mathematics}, year={1998}, volume={156}, pages={467-518} }

We prove that the word problem of a finitely generated group G is in NP (solvable in polynomial time by a nondeterministic 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. This completes the work started in [6] and [25].

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