Guest Column

Finite groups provide an amazing wealth of problems of interest to complexity theory. And complexity theory also provides a useful viewpoint of group-theoretic notions, such as what it means for a group to be \far from abelian." The general problem that we consider in this survey is that of computing a group product g = x1 . x2 ..... xt over a nite group G. Several variants of this problem are considered in this survey and in the literature, including in [KMR, Mi, BC, IL, BGKL, PRS, Am, AL, Raz1, MV, Mi, GV1].