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%W resid.tex FORMAT documentation B. Eick and C.R.B. Wright
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\Chapter{Residual Functions}
%\index{Residual Functions}
\bigskip
\> ResidualWrtFormation( <G>, <F> ) O
Let <G> be a finite solvable group and <F> a formation. Then
`ResidualWrtFormation' returns the -residual subgroup of .
The following special cases have their own functions.
\bigskip
\> NilpotentResidual( <G> ) A
This is the last term of the descending central series of <G>.
\> PResidual( <G>, <p> ) O
This is the smallest normal subgroup of <G> whose index is a power of
the prime <p>.
\> PiResidual( <G>, <primes> ) O
This is the smallest normal subgroup of <G> whose index is divisible
only by primes in the list <primes>.
\> CoprimeResidual( <G>, <primes> ) O
This is the smallest normal subgroup of <G> whose index is
divisible only by primes *not* in the list `primes'.
\> ElementaryAbelianProductResidual( <G> ) 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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