Factoring Elementary p-Groups

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Author: Feit S.W.

Source: Journal of Algebra, Volume 206, Number 1, August 1998 , pp. 170-182(13)

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Abstract:

Let p be an odd prime and let G be an elementary p-group. In other words let G be a direct product of groups of order p. Further let B, A₁,…,A_n be subsets of G such that |B| = p², |A₁| = sdot sdot sdot = |A_n| = p, and each of A₁,…,A_n differs from a subgroup of order p of G in at most one element. If the product BA₁ sdot sdot sdot A_n is direct and is equal to G, then at least one of the factors B, A₁,…,A_n must be periodic. A subset of G is periodic if it is a direct product of a subset and a proper subgroup of G. Copyright 1998 Academic Press.