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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].
MSC:
 20E34 General structure theorems for groups 20D60 Arithmetic and combinatorial problems involving abstract finite groups