<html><head><title>[FORMAT] 3 Residual Functions</title></head>
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<h1>3 Residual Functions</h1><p>
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<li><code>ResidualWrtFormation( </code><var>G</var><code>, </code><var>F</var><code> ) O</code>
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Let <var>G</var> be a finite solvable group and <var>F</var> a formation. Then
<code>ResidualWrtFormation</code> returns the <var>F</var>-residual subgroup of <var>G</var>.
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The following special cases have their own functions.
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<li><code>NilpotentResidual( </code><var>G</var><code> ) A</code>
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This is the last term of the descending central series of <var>G</var>.
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<li><code>PResidual( </code><var>G</var><code>, </code><var>p</var><code> ) O</code>
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This is the smallest normal subgroup of <var>G</var> whose index is a power of
the prime <var>p</var>.
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<li><code>PiResidual( </code><var>G</var><code>, </code><var>primes</var><code> ) O</code>
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This is the smallest normal subgroup of <var>G</var> whose index is divisible
only by primes in the list <var>primes</var>.
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<li><code>CoprimeResidual( </code><var>G</var><code>, </code><var>primes</var><code> ) O</code>
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This is the smallest normal subgroup of <var>G</var> whose index is
divisible only by primes <strong>not</strong> in the list <code>primes</code>.
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<li><code>ElementaryAbelianProductResidual( </code><var>G</var><code> ) A</code>
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This is the smallest normal subgroup of <var>G</var> whose factor group is a
direct product of groups of prime order.
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<address>FORMAT manual<br>January 2024
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