`ResidualWrtFormation( `

`, `

` ) O`

Let `G` be a finite solvable group and `F` a formation. Then
`ResidualWrtFormation`

returns the `F`-residual subgroup of `G`.

The following special cases have their own functions.

`NilpotentResidual( `

` ) A`

This is the last term of the descending central series of `G`.

`PResidual( `

`, `

` ) O`

This is the smallest normal subgroup of `G` whose index is a power of
the prime `p`.

`PiResidual( `

`, `

` ) O`

This is the smallest normal subgroup of `G` whose index is divisible
only by primes in the list `primes`.

`CoprimeResidual( `

`, `

` ) O`

This is the smallest normal subgroup of `G` whose index is
divisible only by primes **not** in the list `primes`

.

`ElementaryAbelianProductResidual( `

` ) A`

This is the smallest normal subgroup of `G` whose factor group is a
direct product of groups of prime order.

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November 2011