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H, N, G are groups

$\displaystyle H \triangleleft N \triangleleft G$ implies $\displaystyle H \triangleleft G$

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- Dec 15th 2009, 03:23 PMElieWieselQuick verification of something...
Is this true?

H, N, G are groups

$\displaystyle H \triangleleft N \triangleleft G$ implies $\displaystyle H \triangleleft G$ - Dec 15th 2009, 04:02 PMtonio
- Dec 15th 2009, 04:39 PMElieWiesel
What if N is cyclic? Does it then imply that H is abelian, and hence H a subgroup of G is normal in G?

- Dec 15th 2009, 05:58 PMtonio