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3%A  additional.tex     AutPGrp documentation                 Bettina Eick
4%A                                                         Eamonn O'Brien
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8\Chapter{Additional Features of the Package}
9
10As an additional feature of this package we provide some functions to
11count extensions of $p$-groups and Lie algebras over $GF(p)$. These
12functions have been used in counting the $2$-groups of size $2^{10}$.
13
14\> NumberOfPClass2PGroups( n, p, k )
15
16determines the number of $n$-generator $p$-groups of $p$-class 2 with
17Frattini subgroup of order $2^k$.
18
19\> NumberOfPClass2PGroups( n, p )
20
21returns a list of of numbers of $n$-generator $p$-groups of $p$-class 2
22with Frattini subgroup of order $2^k$ for $k$ in $1, \ldots, n(n+1)/2$.
23
24\> NumberOfClass2LieAlgebras( n, p, k )
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26determines the number of $n$-generator Lie algebras of class 2 over
27$GF(p)$ with derived Lie subalgebra of dimension $k$.
28
29\> NumberOfClass2LieAlgbras( n, p )
30
31returns a list of of numbers of $n$-generator Lie algebras of class 2
32over $GF(p)$ with derived Lie subalgebra of dimension $k$ for $k$ in
33$1, \ldots, n(n-1)/2$.
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