multiplication = composition = permmul

it is like matrix multiplication that has right or left multiplication

when deal with words

a1*a2*a1^(-1)

it will become a2, how to maintain a1*a2*a1^(-1)

because i expect to do some transformation

permutation matrix
1 1

0 1
become group of permutation

1 1 2

1 2 2

fgen:= convert([1,2,2], disjcyc);

however, first row is not 1,2,3

how to do?

f

1 2 3 4

3 2 4 1

g

1 2 3 4

2 4 3 1
f := permgroup(4, {[[1, 3, 4]], [[2]]});

g := permgroup(4, {[[1, 2, 4]], [[3]]});

mulperms(f,g);
Error, (in permgroup) generators must represent products of disjoint cycles, but [2] does notError, (in permgroup) generators must represent products of disjoint cycles, but [3] does notError, (in convert/plist) bad index into Array

How to use maple to compute the intersection of two permutation group

> test1r := dsolve((Diff(f(x,y), t, t))*x+(Diff(f(x,y), t))*y = 0, f);

Error, (in dsolve) expected an ordinary differential equation. Received: 0 = 0

another question is

i do not know whether can 

 dsolve((Diff(f(x,y), (x,y), (x,y)))*x+(Diff(f(x,y), (x,y)))*y = 0, f);