Let N be a normal subgroup of G , , and C the conjugacy class of a in G .
If is any conjugacy class in G , prove that or .
It is proved that, or .
It is given that N is a normal subgroup of G , , C is the conjugacy class of a in G and is any conjugacy class in G .
If , then there is nothing to prove.
If is non-empty, then part (a) implies that .
It has been concluded that, or .
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