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Abstract: We introduce two new types of Dehn functions of group presentations whichseem more suitable than the standard Dehn function for infinite grouppresentations and prove the fundamental equivalence between the solvability ofthe word problem for a group presentation defined by a decidable set ofdefining words and the property of being computable for one of the newlyintroduced functions this equivalence fails for the standard Dehn function.Elaborating on this equivalence and making use of this function, we obtain acharacterization of finitely generated groups for which the word problem can besolved in nondeterministic polynomial time. We also give upper bounds for thesefunctions, as well as for the standard Dehn function, for two well-knownperiodic groups one of which is an infinite 2-group of intermediate growth andthe other is a free Burnside group of sufficiently large exponent.



Author: R.I. Grigorchuk, S.V. Ivanov

Source: https://arxiv.org/







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