Wednesday, 14 August 2013

Counter examples in group theory

Counter examples in group theory

Let $G$ be a finite group with normal subgroups $N_{1}$ and $N_{2}$. Find
counter examples to the following statements
1) If $N_{1}\cong N_{2}$ then $G/N_{1}\cong G/N_{2}$
2) If $G/N_{1}\cong G/N_{2}$ then $N_{1}\cong N_{2}$.
Thanks for the help.

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