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1. Find which pairs of the following groups are isomorphic: (i) The dihedral group D3 of symmetries of an equilateral triangle. (ii) The group of (complex) matrices 10 01 ω 0 01 0 ω 0 ω 0 0 0 {(69) -(69) (69) (18)-(25)·(25)} under matrix multiplication, where w = C and w³ cube root of unity.) (iii) ZX = {1, 2, 4, 5, 7, 8} under multiplication modulo 9. (iv) Z2 × Z3. = 1,w 1. (That is, w is a particular

1. Find which pairs of the following groups are isomorphic: (i) The dihedral group D3 of symmetries of an equilateral triangle. (ii) The group of (complex) matrices 10 01 ω 0 01 0 ω 0 ω 0 0 0 {(69) -(69) (69) (18)-(25)·(25)} under matrix multiplication, where w = C and w³ cube root of unity.) (iii) ZX = {1, 2, 4, 5, 7, 8} under multiplication modulo 9. (iv) Z2 × Z3. = 1,w 1. (That is, w is a particular

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.CR: Review Exercises
Problem 29CR: Use the standard matrix for counterclockwise rotation in R2 to rotate the triangle with vertices...
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1. Find which pairs of the following groups are isomorphic: (i) The dihedral group D3 of symmetries of an equilateral triangle. (ii) The group of (complex) matrices 10 01 ω 0 01 0 ω 0 ω 0 0 0 {(69) -(69) (69) (18)-(25)·(25)} under matrix multiplication, where w = C and w³ cube root of unity.) (iii) ZX = {1, 2, 4, 5, 7, 8} under multiplication modulo 9. (iv) Z2 × Z3. = 1,w 1. (That is, w is a particular
Transcribed Image Text:1. Find which pairs of the following groups are isomorphic: (i) The dihedral group D3 of symmetries of an equilateral triangle. (ii) The group of (complex) matrices 10 01 ω 0 01 0 ω 0 ω 0 0 0 {(69) -(69) (69) (18)-(25)·(25)} under matrix multiplication, where w = C and w³ cube root of unity.) (iii) ZX = {1, 2, 4, 5, 7, 8} under multiplication modulo 9. (iv) Z2 × Z3. = 1,w 1. (That is, w is a particular
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