57.1 Pq

Pq( F, ... )

Let F be a finitely presented group. Then Pq returns the desired p-quotient of F as an ag group.

The following parameters or parameter pairs are supported.

"Prime", p:

Compute the p-quotient for the prime p.

"ClassBound", n:

The p-quotient computed has lower exponent-p class at most n.

"Exponent", n:

The p-quotient computed has exponent n. By default, no exponent law is enforced.

"Metabelian":

The largest metabelian p-quotient is constructed.

"Verbose":

The runtime-information generated by the ANU pq is displayed. By default, pq works silently.

"OutputLevel", n:

The runtime-information generated by the ANU pq is displayed at output level n, which must be a integer from 0 to 3. This parameter implies "Verbose".

"SetupFile", name:

Do not run the ANU pq, just construct the input file and store it in the file name. In this case true is returned.

Alternatively, you can pass Pq a record as a parameter, which contains as entries some (or all) of the above mentioned. Those parameters which do not occur in the record are set to their default values.

See also PqHomomorphism.

    gap> RequirePackage("anupq");
    gap> f2 := FreeGroup( 2, "f2" );
    Group( f2.1, f2.2 )
    gap> Pq( f2, rec( Prime := 2,  ClassBound := 3 ) );
    Group( G.1, G.2, G.3, G.4, G.5, G.6, G.7, G.8, G.9, G.10 )
    gap> g := f2 / [ f2.1^4, f2.2^4 ];;
    gap> Pq( g, rec( Prime := 2, ClassBound := 3 ) );
    Group( G.1, G.2, G.3, G.4, G.5, G.6, G.7, G.8 )
    gap> Pq( g, "Prime", 2, "ClassBound", 3, "Exponent", 4 );
    Group( G.1, G.2, G.3, G.4, G.5, G.6, G.7 )
    gap> g := f2 / [ f2.1^25, Comm(Comm(f2.2,f2.1),f2.1), f2.2^5 ];;
    gap> Pq( g, "Prime", 5, "Metabelian", "ClassBound", 5 );
    Group( G.1, G.2, G.3, G.4, G.5, G.6, G.7 ) 

This function requires the package "anupq" (see RequirePackage).

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