/*
A presentation for L3(5) in terms of standard generators.
SGens are defined to be (3,5A,20)-generators.
*/

G<x,y>:=Group<x,y|
x^3,
y^5,
x*y*x^-1*y*x*y^-2*x^-1*y*x*y*x^-1*y^-2,
x*y*x^-1*y^-1*x*y^-1*x^-1*y*x*y*x^-1*y*x*y^-1*x^-1*y^-1, // Is redundant.
(y,(y,y^x)),
x*y*x*y*x*y^-1*x*y^2*x*y^2*x*y^-1*x*y*x^-1*y^-2*x^-1*y^-1
>;

M1:=sub<G|y,x*y^2*x*y*x^-1>;
M2:=sub<G|y,x^-1*y*x*y^2*x>;
M3:=sub<G|x,y^-1*x*y*x*y*x*y*x*y^-1>;
M4:=sub<G|x,y*x^-1*y^2*x^-1*y^2*x^-1*y>;
M5:=sub<G|x,y*x^-1*y*x*y^-1*x*y^-1>;

H1:=sub<G|x,y*x^-1*y^2*x^-1*y^2>;
H2:=sub<G|x,y^2*x^-1*y^2*x^-1*y>;
H3:=sub<G|x,y*x*y^2*x*y^-2*x*y^-1*x*y>;

/*
Some other relations that hold:
     x*y*x^-1*y*x*y*x^-1*y^2*x*y^-2*x^-1*y^2,
     x*y*x^-1*y^-1*x*y^-1*x^-1*y*x*y*x^-1*y*x*y^-1*x^-1*y^-1,
and  x*y*x*y*x*y^-1*x*y^2*x*y^2*x^-1*y^-1*x^-1*y^2*x*y^2*x*y^-1
Second of the above is ((y^-1,((y^-1)^(x^-1),y^-1))^y)^-1.
*/