Let G be any group and p: G -G, (g) =g1 Vg eG. Then: (a) o is a homomorphism (b) o is a homomorphism if g is a finite group (c) is a homomorphism if g is abelian (d) o is a homomorphism if and only if g is cyclic

Let G be any group and p: G -G, (g) =g1 Vg eG. Then: (a) o is a homomorphism (b) o is a homomorphism if g is a finite group (c) is a homomorphism if g is abelian (d) o is a homomorphism if and only if g is cyclic

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.5: Isomorphisms

Problem 1E: Prove that if is an isomorphism from the group G to the group G, then 1 is an isomorphism from G to...

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Let G be any group and : G G, (g) =g1 Vg eG. Then:
(a) o is a homomorphism
(b) o is a homomorphism if g is a finite group
(c) is a homomorphism if g is abelian
(d) o is a homomorphism if and only if g is cyclic

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