Let GGL(2,C) be the group of invertible 2 x 2 matrices with entries in the complexnumbers C.001iLet Hbe a group consisting of some of the elements of G0-1 0iWhat is the order of H?Is H isomorphic to Ds?Is Qs, the quaternion group of order 8, isomorphic to Ds as well?

The problem concerns groups of order 8

Answered: Let G GL(2,C) be the group of…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.1: Definition Of A Group

Problem 39E: 39. Let be the set of all matrices in that have the form for arbitrary real numbers , , and ....

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Let G GL(2,C) be the group of invertible 2 x 2 matrices with entries in the complex numbers C. 0 0 1 i Let H be a group consisting of some of the elements of G 0 -1 0 i What is the order of H? Is H isomorphic to Ds? Is Qs, the quaternion group of order 8, isomorphic to Ds as well?