Can you help me to prove this, Let G be a finite Group, and (a € G). Prove that if a has two conjugates in G, then Z(a) normal subgroup of G. ( Z(a) is the central of a )
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Originally Posted by alper82 Can you help me to prove this, Let G be a finite Group, and (a € G). Prove that if a has two conjugates in G, then Z(a) normal subgroup of G. ( Z(a) is the central of a ) Have you come across the orbit-stabiliser theorem? If so, then use this, and remember that a subgroup of index 2 is normal...
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