Description

Sylow complements and Hall subgroups are presently found only for finite solub\ le groups. However while a finite group is soluble iff *all* Sylow complements exist, nonsoluble finite groups may have Sylow complements for *some* primes p\ . (e.g. an alternating group of degree p contains a p Sylow complement.)

The trivial idea to form products of Sylow subgroups obviously is not efficien\ t. Are there methods (such as have been found for Sylow subgroups) to find Sylow complements and more generally Hall subgroups?

To my knowledge not much is known about the existence of Sylow complements in nonsoluble groups, hence to be able to investigate them in examples might be interesting.

For computing, a lifting aproach via the radical would be possible.

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