The Complexity of Iterated Multiplication

For a monoid G the iterated multiplication problem is the computa tion of the product of n elements fromG By re ning known completeness arguments we show that as G varies over a natural series of important groups and monoids the iterated multiplication problems are complete for most natural low level complexity classes The completeness is with respect to rst order projections low level reductions that do not ob scure the algebraic nature of these problems