Abstract
Let G be a finite group written multiplicatively and k a positive integer. If X is a non-empty subset of G, write X 2 = |xy | x, y ∈ X . We say that G has the small square property on k-sets if |X 2| < k 2 for any k-element subset X of G. For each group G, there is a unique m = m G such that G has the small square property on (m + 1)-sets but not on m-sets. In this paper we show that given any positive integer d, there is a finite group G with m G = d.
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Chin, A.Y.M. On Finite Groups and the Small Square Property. Periodica Mathematica Hungarica 40, 205–209 (2000). https://doi.org/10.1023/A:1010395728145
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DOI: https://doi.org/10.1023/A:1010395728145