Theorem 2. Let G; and G, be two groups. Let G = G,x G2H = {(a,e,)|a e G} = G x{e;}%3DH, = {(e.b)beG} = {e}xG,andthen G is an internal direct product of H and H,.

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Answered: Theorem 2. Let G, and G, be two groups.…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.5: Isomorphisms

Problem 34E

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Theorem 2. Let G, and G, be two groups. Let G = G,x G2 H = {(a,e,)\a e G} = G, x{e,} %3D and H, = {(e,.b)b eG,} = {e,)xG, then G is an internal direct product of H, and H,.