Let G be a group. Define a relation on G as follows: I ~ yexists an a EG such that y = ara". (In this case, we say that y is conjugate tois an equivalence relation on G.2.if therex). Prove that(94 points)

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Let G be a group. Define a relation on G as follows: N exists an a EG such that y = axa. (In this case, we say that y is conjugate to 2. y if there x). Prove that ~ is an equivalence relation on G. (24 points)

Let G be a group. Define a relation on G as follows: N exists an a EG such that y = axa. (In this case, we say that y is conjugate to 2. y if there x). Prove that ~ is an equivalence relation on G. (24 points)

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.4: Cyclic Groups

Problem 30E

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Let G be a group. Define a relation on G as follows: I ~ y
exists an a EG such that y = ara". (In this case, we say that y is conjugate to
is an equivalence relation on G.
2.
if there
x). Prove that
(94 points)

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