Answered: For each of the following groups, find…

For each of the following groups, find a non-abelian group where the given group is a distinct normal subgroup of the whole. a) Z2 ⊕ Z2 b) Z3 ⊕ Z3 c) Z3 ⊕ Z2

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.7: Direct Sums (optional)

Problem 11E: 11. Assume that are subgroups of the abelian group such that the sum is direct. If is a subgroup...

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Question

For each of the following groups, find a non-abelian group where the given group is a distinct normal subgroup of the whole.

a) Z₂ ⊕ Z₂

b) Z₃ ⊕ Z₃

c) Z₃ ⊕ Z₂

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