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May 16, 2012 at 13:01 answer added Nick Gill timeline score: 1
May 16, 2012 at 12:49 comment added Wei Zhou Thanks, Nick. I am very interested in the problem discussed in this thread.
May 16, 2012 at 10:47 comment added Nick Gill You might be interested in this thread - mathoverflow.net/questions/96652/cosets-and-conjugacy-classes - where there are some questions concerning the quantity $|a^G\cap C_G(a)|$ .
May 16, 2012 at 6:26 comment added Will Sawin Since the map is always an injection, equal cardinality is the same as surjectivity.
May 16, 2012 at 6:18 comment added Sungjin Kim @Will Sawin, your statement is weaker than the question. because you gave a map from one set to another. However, the question is only asking the equal cardinality statement.
May 16, 2012 at 5:53 vote accept Wei Zhou
May 16, 2012 at 5:40 comment added Will Sawin I think this question would be better phrased: "If $b$ is conjugate to $a$ and in $C_G(a)$, then there exists $c\in N_G(C_G(a))$ such that $b=cac^{-1}$."
May 16, 2012 at 4:45 answer added Jeremy Rickard timeline score: 6
May 16, 2012 at 3:28 history asked Wei Zhou CC BY-SA 3.0