37.7 The Solvable Groups Library

GAP has a library of the 1045 solvable groups of size between 2 and 100. The groups are from lists computed by M.~Hall and J.~K.~Senior (size 64, see HS64), R.~Laue (size 96, see Lau82) and J.~Neubaccent127user (other sizes, see Neu67).

AllSolvableGroups( fun1, val1, fun2, val2, ... )

AllSolvableGroups returns a list containing all solvable groups that have the properties given as arguments. Each property is specified by passing a pair of arguments, the first being a function, which will be applied to all the groups in the library, and the second being a value or a list of values, that this function must return in order to have this group included in the list returned by AllSolvableGroups.

    gap> AllSolvableGroups(Size,24,IsNontrivialDirectProduct,false);
    [ 12.2, grp_24_11, D24, Q8+S3, Sl(2,3), S4 ] 

OneSolvableGroup( fun1, val1, fun2, val2, ... )

OneSolvableGroup returns a solvable group with the specified properties. Each property is specified by passing a pair of arguments, the first being a function, which will be applied to all the groups in the library, and the second being a value or a list of values, that this function must return in order to have this group returned by OneSolvableGroup. If no such group exists, false is returned.

    gap> OneSolvableGroup(Size,100,x->Size(DerivedSubgroup(x)),10);
    false
    gap> OneSolvableGroup(Size,24,IsNilpotent,false);
    S3x2^2 

AllSolvableGroups and OneSolvableGroup recognize the following functions and handle them usually very efficiently: Size, IsAbelian, IsNilpotent, and IsNonTrivialDirectProduct.

SolvableGroup( size, nr )

SolvableGroup returns the nr-th group of size size in the library. SolvableGroup will signal an error if size is not between 2 and 100, or if nr is larger than the number of solvable groups of size size. Finite Polycyclic Groups).

    gap> SolvableGroup( 32 , 15 );
    Q8x4 

Previous Up Top Next
Index