Factoring small 2-groups

Abstract

Let G be a finite abelian group and let G = A_1 · · · A_n  be a factorization of G into its subsets A_1 , . . . , A_n. For a given G certain choices of the orders |A_1|, . . . , |A_n| guarantee that one of the factors is periodic. In connection with an open problem we determine such choices of orders of factors in
two special cases. In these cases |G| is either  2^5 or  2^6 .