Pseudo-free families of finite computational elementary abelian p-groups

Abstract

Abstract We initiate the study of (weakly) pseudo-free families of computational elementary abelian p-groups, where p is an arbitrary fixed prime. We restrict ourselves to families of computational elementary abelian p-groups G d {G_{d}} such that for every index d, each element of G d {G_{d}} is represented by a single bit string of length polynomial in the length of d. First, we prove that pseudo-freeness and weak pseudo-freeness for families of computational elementary abelian p-groups are equivalent. Second, we give some necessary and sufficient conditions for a family of computational elementary abelian p-groups to be pseudo-free (provided that at least one of two additional conditions holds). Third, we establish some necessary and sufficient conditions for the existence of pseudo-free families of computational elementary abelian p-groups.