Linear and sublinear time algorithms for the basis of abelian groups

It is well known that every finite abelian group G can be represented as a direct product of cyclic groups: G ≅ G 1 × G 2 × ⋯ × G t , where each G i is a cyclic group of order p j for some prime p and integer j ≥ 1 . If a i generates the cyclic group of G i , i = 1 , 2 , … , t , then the elements a...

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