The Functional Equation max{?(xy),?(xy-1)}=?(x)?(y) on Groups and Related Results

This research paper focuses on the investigation of solutions ?:G?R maximum functional equation max{?(xy),?(xy?1)}=?(x)?(y), for every x,y?G, where G is any group. We determine that if a group divisible by two and three, then non-zero solution necessarily strictly positive; work Toborg, we can conclude are exactly e|?| an additive function ?:G?R. Moreover, our yields reliable to G, instead being three. also prove existence normal subgroups Z? N? satisfy some properties, be interpreted as abelian factor G/N?.