Large and small sets with respect to homomorphisms and products of groups

[EN] We study the behaviour of large, small and medium subsets with respect to homomorphisms and products of groups. Then we introduce the definition af a P-small set in abelian groups and we investigate the relations between this kind of smallness and the previous one, giving some examples that distinguish them.Gusso, R. (2002). Large and small sets with respect to homomorphisms and products of groups. Applied General Topology. 3(2):133-143. doi:10.4995/agt.2002.2059.13314332Cotlar, M., & Ricabarra, R. (1954). On the Existence of Characters in Topological Groups. American Journal of Mathematics, 76(2), 375. doi:10.2307/2372579Dikran N. Dikranjan, Ivan R. Prodanov, Luchezar N. Stoyanov, Topological Groups: Characters, Dualities and Minimal Group Topologies, Pure and Applied Mathematics, Vol. 130 (Marcel Dekker Inc. New York-Basel, 1989).Ellis, R., & Keynes, H. B. (1972). Bohr compactifications and a result of følner. Israel Journal of Mathematics, 12(3), 314-330. doi:10.1007/bf02790758Følner, E. (1955). On groups with full Banach mean value. MATHEMATICA SCANDINAVICA, 3, 243. doi:10.7146/math.scand.a-1044