Factoring an elementary 2-group into normalized full-rank subsets with equal sizes

摘要

By a long standing conjecture of Redei if an elementary p-group of rank 3 is a direct product of two of its normalized subsets, then at least one of the factors is contained in a subgroup of order p(2). Motivated by Redei's conjecture we decompose an elementary 2-group into a direct product of more than two factors such that each factor spans the whole group.