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Prove that if G is a finite group, the index of Z(G)
Chapter 7, Problem 38E(choose chapter or problem)
Prove that if G is a finite group, the index of Z(G) cannot be prime.
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QUESTION:
Prove that if G is a finite group, the index of Z(G) cannot be prime.
ANSWER:Step 1 of 3
Suppose G be a finite group.
The aim of this problem is to prove that the index of Z(G) cannot be prime, that is, \([G: Z(G)]\) cannot be prime.
Step 2 of 3
Recall the G/Z Theorem: Suppose G be a group with center Z(G). If G/Z(G) is cyclic, then G
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