Small P-Groups with Full-Rank Factorization

The problem of determining which abelian groups admit a full-rank normalized factorization is settled for the orders 64 = 26, 81 = 34, and 128 = 27. By a computer-aided approach, it is shown that such groups of these orders are exactly those of type (22,22,22), (22,22,2,2), (23,22,22), (23,22,2,2), (22,22,22,2), and (22,22,2,2,2).

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