Pseudo-free families of finite computational elementary abelian p-groupsстатья
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Аннотация: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 $G_d$ such that for every index $d$, each element of $G_d$ 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.