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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 <i>p</i>-groups and Lie algebras over <i>GF</i>(<i>p</i>). These
functions have been used in counting the 2-groups of size 2<sup>10</sup>.
<p>
<a name = ""></a>
<li><code>NumberOfPClass2PGroups( n, p, k )</code>
<p>
determines the number of <i>n</i>-generator <i>p</i>-groups of <i>p</i>-class 2 with
Frattini subgroup of order 2<sup><i>k</i></sup>.
<p>
<a name = ""></a>
<li><code>NumberOfPClass2PGroups( n, p )</code>
<p>
returns a list of of numbers of <i>n</i>-generator <i>p</i>-groups of <i>p</i>-class 2
with Frattini subgroup of order 2<sup><i>k</i></sup> for <i>k</i> in 1, …, <i>n</i>(<i>n</i>+1)/2.
<p>
<a name = ""></a>
<li><code>NumberOfClass2LieAlgebras( n, p, k )</code>
<p>
determines the number of <i>n</i>-generator Lie algebras of class 2 over
<i>GF</i>(<i>p</i>) with derived Lie subalgebra of dimension <i>k</i>.
<p>
<a name = ""></a>
<li><code>NumberOfClass2LieAlgbras( n, p )</code>
<p>
returns a list of of numbers of <i>n</i>-generator Lie algebras of class 2
over <i>GF</i>(<i>p</i>) with derived Lie subalgebra of dimension <i>k</i> for <i>k</i> in
1, …, <i>n</i>(<i>n</i>−1)/2.
<p>
<p>
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<P>
<address>AutPGrp manual<br>April 2025
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