(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let A be a normal subgroup of a group G, with A cyclic and G/A nonabelian simple. Prove that Z(G)= A

2. Relevant equations

Z(G) = A <=> C_{G}(G) = A = {a in G: ag = ga for all g in G}

My professor's hint was "what is G/C_{G}(A)?"

3. 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.

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# Homework Help: Group Theory Question involving nonabelian simple groups and cyclic groups

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