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Questions on set squaring in groups. (English) Zbl 0945.20015
Deshouillers, Jean-Marc (ed.) et al., Structure theory of set addition. Paris: Société Mathématique de France, Astérisque. 258, 249-253 (1999).
Let \(M\) be a subset of a group \(G\). Define \(M^2=\{x\mid x=ab,\;a,b\in M\}\), the square of \(M\). \(M\) is a set with a large square if \(\forall a,b,c,d\in M\), \(ab=cd\) implies \(a=c\), \(b=d\), in the opposite case \(M\) is said to be a set with small square. In this short paper, some interesting questions on small subsets in groups are posed and discussed.
For the entire collection see [Zbl 0919.00044].
20E34 General structure theorems for groups
20D60 Arithmetic and combinatorial problems involving abstract finite groups