Characterization of abelian groups
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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
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Solution Summary
The expert examines a characterization of abelian groups. A new group H element is defined.
Education
- AB, Hood College
- PhD, The Catholic University of America
- PhD, The University of Maryland at College Park
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