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paddyoneil
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Homework Statement
Let A be a normal subgroup of a group G, with A cyclic and G/A nonabelian simple. Prove that Z(G)= A
Homework Equations
Z(G) = A <=> CG(G) = A = {a in G: ag = ga for all g in G}
My professor's hint was "what is G/CG(A)?"
The Attempt at a Solution
A is cyclic => A is abelian
A normal in G <=> gAg-1 = A
So gA=Ag. Then gA is an element of G/A.
I don't really know where to go. I have been working on this for several hours and am at a loss. Any help would be greatly appreciated.