Suppose that G is a non-Abelian group of order \(p ^ { 3 }\) where p is prime and \(Z ( G ) \neq \{ e \}\) . Prove that \(| Z ( G ) | = p\) .
Center of a non-abelian group of order $p^3$
P-CH9S-049
- Area
- Algebra
- Status
- draft
P-CH9S-049
Suppose that G is a non-Abelian group of order \(p ^ { 3 }\) where p is prime and \(Z ( G ) \neq \{ e \}\) . Prove that \(| Z ( G ) | = p\) .