Why do the conjugate classes of a group partition the group?

  • #1
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Given an element a in a group G,
class(a) = {all x in G such that there exists a g in G such that gxg^(-1) = a}

class(b) = {all x in G such that there exists a g in G such that gxg^(-1) = b}

so let's say y is a conjugate of both a and b, so it is in both class(a) and class(b), does that mean that class(a) = class(b)?

given there is an element y that is in both class(a) and class(b), couldn't there be an element q that is in one class and not the other?
 

Answers and Replies

  • #2
784
11
I answered my own question, can't figure out how to delete this
 

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