On Dehn functions of infinite presentations of groups

Mathematics – Group Theory

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

27 pages, 4 figures; to appear in GAFA

Scientific paper

We introduce two new types of Dehn functions of group presentations which seem more suitable (than the standard Dehn function) for infinite group presentations and prove the fundamental equivalence between the solvability of the word problem for a group presentation defined by a decidable set of defining words and the property of being computable for one of the newly introduced functions (this equivalence fails for the standard Dehn function). Elaborating on this equivalence and making use of this function, we obtain a characterization of finitely generated groups for which the word problem can be solved in nondeterministic polynomial time. We also give upper bounds for these functions, as well as for the standard Dehn function, for two well-known periodic groups one of which is an infinite 2-group of intermediate growth and the other is a free Burnside group of sufficiently large exponent.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

On Dehn functions of infinite presentations of groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On Dehn functions of infinite presentations of groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Dehn functions of infinite presentations of groups will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-175995

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.