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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Please answer question 10, 11 and 12. Answer if TRUE or FALSE only.
![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' (p(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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9e69f71c-493f-4e8c-97ca-6b833368d1d8%2Fb0095afe-3541-4412-aab2-e9a0a83824bf%2Fof7gck_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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' (p(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
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