Let G be a group (written additively), S a nonempty set and M (S, G) the set of all functions from S in G. We define addiction in M (S, G) as follows: For ?, ? ∈ ? (S, G) and for each s ∈ S, (f + g) (s) = f (s) + g (s). Prove that M (S, G) is a group with this operation, and that it is abelian if and only if G

Let G be a group (written additively), S a nonempty set and M (S, G) the set of all functions from S in G. We define addiction in M (S, G) as follows: For ?, ? ∈ ? (S, G) and for each s ∈ S, (f + g) (s) = f (s) + g (s). Prove that M (S, G) is a group with this operation, and that it is abelian if and only if G

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.4: Cyclic Groups

Problem 31E: Exercises 31. Let be a group with its center: . Prove that if is the only element of order in ,...

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