Sur un problème au sujet des homomorphismes. (On a problem concerning homomorphisms)
Let f and g be homomorphisms from the additive group \((R,+)\) into a group (G,\(\cdot)\). The author considers the problem, when the relation \((1)\quad \bigwedge_{t\in R}f(t)g(t)=g(t)f(t)\) implies the condition \((2)\quad \bigwedge_{t,s\in R}f(t)g(s)=g(s)f(t).\) The author gives some conditions for homomorphisms f,g and group G which ensure the above implication. Moreover it is given an example of a group G, with the following property: for every linear subspace P of R over Q with codim \(P\geq 2\), there exist homomorphisms f and g from \((R,+)\) into (G,\(\cdot)\) satisfying (1) and \(\bigvee_{s,t\in R}f(s)g(t)\neq g(t)f(s)\) and Ker f\(=Ker g=P\).
scientific article; zbMATH DE number 4038394