1.) Let G₁ = £1₁ 1₁ i-i) becomplex mumbersgroup of 4under mutiplication.a) is [1, i} a subgroup 6/7/why?b.) 15 £1,1} a subgroup & and why?

Given group under multiplicationG = 1, -1, i , -i A subset H of G will be subgroup of G if H…

Answered: 1.) Let G₁ = £1₁ 1₁ i -i) be group of 4…

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 9E: Let be a subgroup of a group with . Prove that if and only if

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1.) Let G₁ = £1₁ 1₁ i -i) be group of 4 Complex numbers under mutiplication. a) is £1, i} a subgroup 6 // why? b.) is £1,1} a subgroup for and why?