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}.
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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