Conclusion
Many questions remain unanswered. Probably the most difficult and intriguing is the problem of finding necessary and sufficient conditions for a member of S to have an n-th root if n is an integer greater than 1. One may also ask, on which subsets of S is the n-th power function one-to-one?
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Communicated by 0. R. Brown
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Howard, H.L. Roots of increasing sequences. Semigroup Forum 14, 167–173 (1977). https://doi.org/10.1007/BF02194664
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DOI: https://doi.org/10.1007/BF02194664