Comparing the Computational Complexity of Monomials and Elements of Finite Abelian Groups

The computational complexity of the element of the Abelian group (it is supposed that for all ) and the computational complexity of the term are compared in the paper. The computational complexity means the minimal possible number of multiplication operations, and all the results of intermediate multiplications can be used multiple times. It is established that, if , then the maximal possible difference and ratio of the above values asymptotically grow for as and , respectively.