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I know some facts such as: Nilpotent groups are solvable, $p$-groups are nilpotent, a finite group whose order is a product of distinct primes is solvable, and finite groups are nilpotent if and only if it is a finite product of solvable groups.

Are there any other major relationships between these concepts that one should be aware of?

Also, how do you compute a transfer? Could you provide a simple example or two?

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    Probably, he thinks that all groups are finite. For me that's also true ;-)2012-12-12

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