Prove the following statement1.19. If M and N are normal subgroups of a group G, then G/(MO N)is isomorphic to a subgroup of the (external) direct product G/M X G/N.

Given : M and N are normal subgroups of a group G. To prove : G/M∩N is isomorphic to G/M × G/N.

Answered: 1.19. If M and N are normal subgroups…

1.19. If M and N are normal subgroups of a group G, then G/(MN) is isomorphic to a subgroup of the (external) direct product G/MXG/N.

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 20E

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Question

Prove the following statement
1.19. If M and N are normal subgroups of a group G, then G/(MO N)
is isomorphic to a subgroup of the (external) direct product G/M X G/N.

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