5.1 In each case, determine whether or not H is a subgroup of G.a) G=(R, +); H=Qb) G=(Q, +); H=Zc) G=(Z, +); H=Z*d) G=(Q-(0}, ); H=Q+e) G=(Zg, Ð); H=(0,2,4}f) G=the set of 2-tuples of real numbers (a,b) under addition of 2-tuples;H=the subset consisting of all 2-tuples such that b=-ag) G=Qs; H={I, J, K}h) G=(P(X), A); H={Ø, A, B, A AB}, where A, B are two elements of Gi) G=(P(X), A); H=P(Y), where YCX.

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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 32E: (See Exercise 31.) Suppose G is a group that is transitive on 1,2,...,n, and let ki be the subgroup...

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5.1 In each case, determine whether or not H is a subgroup of G. a) G=(R, +); H=Q b) G=(Q, +); H=Z c) G=(Z, +); H=Z* d) G=(Q-(0}, ); H=Q*