5. The following statements are made about (right) cosets of a subgroup H of a group G. Say whether each statement is true or false and give a reason for your answer. (i) H itself is a coset. (ii) Every element of G belongs to a coset. (iii) If y is in a coset Hx, then Hy = Hx. (iv) Two cosets Hx and Hy are either the same, or they are disjoint, HxHy = 0). 1 (v) Hx = Hy if and only if xy-¹ € H.

5. The following statements are made about (right) cosets of a subgroup H of a group G. Say whether each statement is true or false and give a reason for your answer. (i) H itself is a coset. (ii) Every element of G belongs to a coset. (iii) If y is in a coset Hx, then Hy = Hx. (iv) Two cosets Hx and Hy are either the same, or they are disjoint, HxHy = 0). 1 (v) Hx = Hy if and only if xy-¹ € H.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.4: Cosets Of A Subgroup

Problem 12E: Let H and K be subgroups of a group G and K a subgroup of H. If the order of G is 24 and the order...

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