Problem 1. In each of the following, either prove or disprove that the given subsetHis a subgroup of G.1.1. G = (Q,+) and H = { : a, d = Z with d\n}, where n € Z+ is fixed.1.2. GS10, and H = {σ = S10 : |σ| = 4} U {e}.1.3. G = GL2(R) andH={ ( a ) : a: a, b, c € R with ac 40}.

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Answered: Problem 1. In each of the following,…

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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Problem 1. In each of the following, either prove or disprove that the given subset His a subgroup of G. 1.1. G = (Q,+) and H = { : a, d = Z with d\n}, where n € Z+ is fixed. 1.2. GS10, and H = {σ = S10 : |σ| = 4} U {e}. 1.3. G = GL2(R) and H = { ( a ) : a : a, b, c € R with ac 40}.