additional.tex

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%A  additional.tex     AutPGrp documentation                 Bettina Eick
%A                                                         Eamonn O'Brien
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\Chapter{Additional Features of the Package}

As an additional feature of this package we provide some functions to
count extensions of $p$-groups and Lie algebras over $GF(p)$. These
functions have been used in counting the $2$-groups of size $2^{10}$.

\> NumberOfPClass2PGroups( n, p, k )

determines the number of $n$-generator $p$-groups of $p$-class 2 with
Frattini subgroup of order $2^k$. 

\> NumberOfPClass2PGroups( n, p )

returns a list of of numbers of $n$-generator $p$-groups of $p$-class 2
with Frattini subgroup of order $2^k$ for $k$ in $1, \ldots, n(n+1)/2$.

\> NumberOfClass2LieAlgebras( n, p, k )

determines the number of $n$-generator Lie algebras of class 2 over 
$GF(p)$ with derived Lie subalgebra of dimension $k$.

\> NumberOfClass2LieAlgbras( n, p )

returns a list of of numbers of $n$-generator Lie algebras of class 2
over $GF(p)$ with derived Lie subalgebra of dimension $k$ for $k$ in
$1, \ldots, n(n-1)/2$.

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