Let a group G be the internal direct product of two its subgroups H\index{1} and H\index{2}. Then H\index{1} and H\index{2} are the normal subgroups of G and G/H\index{1}≅H\index{2} and G/H\index{2}≅H\index{1}
Let a group G be the internal direct product of two its subgroups H\index{1} and H\index{2}. Then H\index{1} and H\index{2} are the normal subgroups of G and G/H\index{1}≅H\index{2} and G/H\index{2}≅H\index{1}
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 22E: 22. If and are both normal subgroups of , prove that is a normal subgroup of .
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Let a group G be the internal direct product of two
its subgroups H\index{1} and H\index{2}. Then H\index{1} and H\index{2} are the
normal subgroups of G and
G/H\index{1}≅H\index{2} and G/H\index{2}≅H\index{1}.
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