a. Show that the function f : G ----> defined by f(x) = x^(-1) is a group homomorphism if and only if G is abelian
b. Define a new group H to have the same elements as G, but the operation x # y = yx, where yx is defined by the operation in G. Show that the function f : G ----> H defined by f (x) = x ^ (-1) is an isomorphism of G onto H© BrainMass Inc. brainmass.com October 10, 2019, 2:52 am ad1c9bdddf
The expert examines a characterization of abelian groups. A new group H element is defined.