Answered: Let G be a group and let H and K be…

Let G be a group and let H and K be normal subgroups such that HnK={e}. Let : G→G/HxG/K be the map (g) = (Hg, Kg). Prove that the kernel of ois {e}.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.5: Normal Subgroups

Problem 4E: 4. Prove that the special linear group is a normal subgroup of the general linear group .

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Question

Let G be a group and let H and K be normal subgroups such that HnK={e}. Let
: G→G/HxG/K be the map (g) = (Hg, Kg).
Prove that the kernel of ois {e}.

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