  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.
