COMPUTATIONS OVER INFINITE GROUPS

We propose the study of a wide variety of infinite groups from a computational complexity point of view. We raise some important structural questions on these groups from a computational aspect. The purpose of this paper is to invite the attention of both the theoretical computer science community and the combinatorial group theorists that a fruitful area of cross fertilization may be offering itself. As a specific problem, we consider randomly generated groups and their isomorphism problem.