Let G be a group and H be a subgroup of G. We can tell if H is normal in G by determining if: aHa-1 = {aha-1: h ∈ H} is equal to H for every a ∈ G. Let H = <R2> in the group D6 of symmetries of a regular hexagon. Determine the elements in rHr-1Let K = <r> in D6. Determine the elements of (rR)K(rR)-1

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Let G be a group and H be a subgroup of G. We can tell if H is normal in G by determining if: aHa-1 = {aha-1: h ∈ H} is equal to H for every a ∈ G. Let H = in the group D6 of symmetries of a regular hexagon. Determine the elements in rHr-1 Let K = in D6. Determine the elements of (rR)K(rR)-1

Let G be a group and H be a subgroup of G. We can tell if H is normal in G by determining if: aHa-1 = {aha-1: h ∈ H} is equal to H for every a ∈ G. Let H = in the group D6 of symmetries of a regular hexagon. Determine the elements in rHr-1 Let K = in D6. Determine the elements of (rR)K(rR)-1

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.6: Quotient Groups

Problem 19E

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Question

Let G be a group and H be a subgroup of G. We can tell if H is normal in G by determining if: aHa^-1 = {aha^-1: h ∈ H} is equal to H for every a ∈ G.

Let H = <R²> in the group D₆ of symmetries of a regular hexagon. Determine the elements in rHr^-1

Let K = <r> in D₆. Determine the elements of (rR)K(rR)^-1

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