Small product sets in groups P × G
Conjuntos producto pequeño en grupos P × G
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Some problems in number theory can be studied in more general algebraic structures. One of them is the small product sets problem, which consists of finding the minimum cardinality of the set AB, where A and B are non-empty subsets of a group G, of fixed cardinalities. This problem was solved for abelian groups, however, a general solution is not known for the class of non-abelian groups. In this article, we study this problem for groups of the form G=P×G, where P is a finite group and A is an abelian group. As a particular case, we solve the small product sets problem in the class of infinite Hamiltonian groups.
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