A Let (A, +,.) be a subgroup of (M₂ (Z), +,.), Then A is ideal of M₂ (Z), where = {(ab) a, b, c € Z}.
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- 18. If is a subgroup of the group such that for all left cosets and of in, prove that is normal in.5. For any subgroup of the group , let denote the product as defined in Definition 4.10. Prove that corollary 4.19:4. Prove that the special linear group is a normal subgroup of the general linear group .
- 19. With and as in Exercise 18, prove that is a subgroup of . Exercise18: 18. If is a subgroup of , and is a normal subgroup of , prove that .9. Suppose that and are subgroups of the abelian group such that . Prove that .Prove or disprove that H={ hGh1=h } is a subgroup of the group G if G is abelian.