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Basic Operations


Basic Operations






Subsections



Accessing Group Information






The functions in this group provide access to basic information 
stored for a group G.



G . i : Grp, RngIntElt -> GrpElt



The i-th defining generator for G, if i>0. If i<0, then the
inverse of the -i-th defining generator is returned.
G.0 is equivalent to Identity(G).



Generators(G) : Grp -> { GrpFinElt }



A set containing the defining generators for G.



NumberOfGenerators(G) : Grp -> RngIntElt


Ngens(G) : Grp -> RngIntElt



The number of defining generators for G.



Generic(G) : Grp -> Grp



The generic group containing G, i.e., the largest group in which G
is naturally embedded. The precise definition of generic group
depends upon the category to which G belongs.



Parent(g) : GrpElt -> Grp



The parent group G for the group element g.





Example Grp_Generators (H15E10)

The Suzuki simple group G=Sz(8) is constructed.
Its generic group is GL(4, K),
where K is the finite field with 8 elements.
The field K is constructed first,
so that its generator may be given the printname z.
Then the three generators of G are printed,
in the standard order of indexing.





> K<z> := GF(2, 3);
> G := SuzukiGroup(8);         
> Generic(G);
GL(4, GF(2, 3))
> Ngens(G);
3
> for i in [1..3] do
>    print "generator", i, G.i;                      
>    print "order", Order(G.i), "\r";
> end for;
generator 1 
[  0   0   0   1]
[  0   0   1   0]
[  0   1   0   0]
[  1   0   0   0]
order 2 




generator 2 
[z^2   0   0   0]
[  0 z^6   0   0]
[  0   0   z   0]
[  0   0   0 z^5]
order 7 




generator 3 
[  1   0   0   0]
[z^2   1   0   0]
[  0   z   1   0]
[z^5 z^3 z^2   1]
order 4 





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