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Show that E In = {z Є C such that z" = 1, n E Z}, is a subgroup of the group S₁ = {z E C such that |z| = 1, Is In a normal subgroup of $1 ? Explain. n E Z}

Show that E In = {z Є C such that z" = 1, n E Z}, is a subgroup of the group S₁ = {z E C such that |z| = 1, Is In a normal subgroup of $1 ? Explain. n E Z}

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter4: More On Groups
Section4.5: Normal Subgroups
Problem 4E: 4. Prove that the special linear group is a normal subgroup of the general linear group .
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Show that E In = {z Є C such that z" = 1, n E Z}, is a subgroup of the group S₁ = {z E C such that |z| = 1, Is In a normal subgroup of $1 ? Explain. n E Z}
Transcribed Image Text:Show that E In = {z Є C such that z" = 1, n E Z}, is a subgroup of the group S₁ = {z E C such that |z| = 1, Is In a normal subgroup of $1 ? Explain. n E Z}
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