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<html><head><title>[AutPGrp] 5 Additional Features of the Package</title></head>
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<h1>5 Additional Features of the Package</h1><p>
<p>
As an additional feature of this package we provide some functions to
count extensions of <var>p</var>-groups and Lie algebras over <var>GF(p)</var>. These
functions have been used in counting the <var>2</var>-groups of size <var>2<sup>10</sup></var>.
<p>
<a name = ""></a>
<li><code>NumberOfPClass2PGroups( n, p, k )</code>
<p>
determines the number of <var>n</var>-generator <var>p</var>-groups of <var>p</var>-class 2 with
Frattini subgroup of order <var>2<sup>k</sup></var>.
<p>
<a name = ""></a>
<li><code>NumberOfPClass2PGroups( n, p )</code>
<p>
returns a list of of numbers of <var>n</var>-generator <var>p</var>-groups of <var>p</var>-class 2
with Frattini subgroup of order <var>2<sup>k</sup></var> for <var>k</var> in <var>1, ..., n(n+1)/2</var>.
<p>
<a name = ""></a>
<li><code>NumberOfClass2LieAlgebras( n, p, k )</code>
<p>
determines the number of <var>n</var>-generator Lie algebras of class 2 over
<var>GF(p)</var> with derived Lie subalgebra of dimension <var>k</var>.
<p>
<a name = ""></a>
<li><code>NumberOfClass2LieAlgbras( n, p )</code>
<p>
returns a list of of numbers of <var>n</var>-generator Lie algebras of class 2
over <var>GF(p)</var> with derived Lie subalgebra of dimension <var>k</var> for <var>k</var> in
<var>1, ..., n(n-1)/2</var>.
<p>
<p>
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<P>
<address>AutPGrp manual<br>Februar 2010
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