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2. For each of the following parts, K is a subgroup of the group G. Write down every element of every (distinct) right coset AND every distinct left coset. You do not need to prove that you have found every coset. (a) K = {ro, 790°, 7180°, 790), G is D₁, the set of symmetries of the square. For the sake of notation, denote the reflections of the square as se, Sh, SNW and SNE (b) K = {e, (12)}, G = S3 (Ⓒ) K = ([id]). G= G = GL2(Z₂). For your convenience, the elements of GL2(Z2) are given below. You may use the given letters to refer to them: GL₁2 (22) = {1=[bi] = [id], ₁-6--8}} a=

2. For each of the following parts, K is a subgroup of the group G. Write down every element of every (distinct) right coset AND every distinct left coset. You do not need to prove that you have found every coset. (a) K = {ro, 790°, 7180°, 790), G is D₁, the set of symmetries of the square. For the sake of notation, denote the reflections of the square as se, Sh, SNW and SNE (b) K = {e, (12)}, G = S3 (Ⓒ) K = ([id]). G= G = GL2(Z₂). For your convenience, the elements of GL2(Z2) are given below. You may use the given letters to refer to them: GL₁2 (22) = {1=[bi] = [id], ₁-6--8}} a=

Elements Of Modern Algebra
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 2E: For each of the following subgroups H of the addition groups Z18, find the distinct left cosets of H...
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2. For each of the following parts, K is a subgroup of the group G. Write down every element of every (distinct) right coset AND every distinct left coset. You do not need to prove that you have found every coset. (a) K = {ro, 1900, 1800, 1900), G is D4, the set of symmetries of the square. For the sake of notation, denote the reflections of the square as S, Sh, SNW and SNE. (b) K = {e, (12)}, G = S3 (c) K = ([i]), G = GL2(Z₂). For your convenience, the elements of GL2(Z2) are given below. You may use the given letters to refer to them: GL₂Z) --------3-80 GL2(Z2) = C= (d) K = (5), G = Z₁2 = a= b= f
Transcribed Image Text:2. For each of the following parts, K is a subgroup of the group G. Write down every element of every (distinct) right coset AND every distinct left coset. You do not need to prove that you have found every coset. (a) K = {ro, 1900, 1800, 1900), G is D4, the set of symmetries of the square. For the sake of notation, denote the reflections of the square as S, Sh, SNW and SNE. (b) K = {e, (12)}, G = S3 (c) K = ([i]), G = GL2(Z₂). For your convenience, the elements of GL2(Z2) are given below. You may use the given letters to refer to them: GL₂Z) --------3-80 GL2(Z2) = C= (d) K = (5), G = Z₁2 = a= b= f
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