Summary
A factorization of a finite abelian group is said to be simulated if it is obtained from a factorization into a direct product of subgroups by changing at mostk elements in each subgroup. The question has been asked as to which values ofk imply that in fact at least one subgroup must be left unaltered. This has been shown to be true fork = 1 but to be false, in general, fork = p − 1, wherep is the least prime dividing the order ofG. In this paper it is shown to be true fork = p − 2.
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Sands, A.D. Simulated factorizations II. Aeq. Math. 44, 48–59 (1992). https://doi.org/10.1007/BF01834204
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DOI: https://doi.org/10.1007/BF01834204