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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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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
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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