On groups that have normal forms computable in logspace
Group Theory
2014-01-28 v3 Computational Complexity
Abstract
We consider the class of finitely generated groups which have a normal form computable in logspace. We prove that the class of such groups is closed under finite extensions, finite index subgroups, direct products, wreath products, and also certain free products, and includes the solvable Baumslag-Solitar groups, as well as non-residually finite (and hence non-linear) examples. We define a group to be logspace embeddable if it embeds in a group with normal forms computable in logspace. We prove that finitely generated nilpotent groups are logspace embeddable. It follows that all groups of polynomial growth are logspace embeddable.
Cite
@article{arxiv.1201.4363,
title = {On groups that have normal forms computable in logspace},
author = {Murray Elder and Gillian Elston and Gretchen Ostheimer},
journal= {arXiv preprint arXiv:1201.4363},
year = {2014}
}
Comments
24 pages, 1 figure. Minor corrections from previous version