10. The set of automorphisms of a group is a group under the operation of function composition. True False 11. Suppose that is an isomorphism from a group G onto a group G'. Then G = (a) if and only if G' = ((a)). True False 12. Suppose that is an isomorphism from a group G onto a group G'. Then G is Abelian if and only if G' is Abelian. ● True ● False

10. The set of automorphisms of a group is a group under the operation of function composition. True False 11. Suppose that is an isomorphism from a group G onto a group G'. Then G = (a) if and only if G' = ((a)). True False 12. Suppose that is an isomorphism from a group G onto a group G'. Then G is Abelian if and only if G' is Abelian. ● True ● False

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.6: Quotient Groups

Problem 32E: 32. Let be a fixed element of the group . According to Exercise 20 of section 3.5, the mapping ...

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