[GAP Forum] Random elements of a permutation group.

[Kieran Roberts]

Hello,

I opened two instances of GAP on two different machines. I ran the
following code on both instances:

G := SymmetricGroup(15);;
for i in [ 1 .. 20 ] do
    Display(Random(G));
od;

And both produced the same list of elements:

( 1,11, 4, 3,15,10, 5, 9, 7,14,12,13)( 6, 8)
( 1,10,13,12, 3, 9, 2, 7, 6, 5, 8,14,15,11)
( 1,10,12, 6, 4,14, 5, 2,11,15, 7)( 8, 9,13)
( 1, 4,13, 9, 8, 6,15, 5,11,10)( 2, 7,14, 3)
( 2, 5, 6)( 3, 4, 8)( 7,12,15,14,10, 9)
( 1, 5, 9, 8)( 2,13,11,14, 4, 6)( 3,10,15, 7,12)
( 1,11, 2)( 3, 4,14,15,12, 6, 9, 5, 8, 7,13,10)
( 1,15, 4)( 2, 3,12, 7,11,13, 5, 6, 8,14,10)
( 1,13, 8, 6,12,14, 2,11, 9, 4)( 3,10)( 5, 7)
( 2, 5, 6,13, 8,12, 4, 9,15,10, 7,14)
( 1,15)( 2, 3,10,11, 6,13, 4, 7, 9, 8,12)
( 1,10)( 2, 6, 4, 7,13,15, 9,14)( 3, 8)
( 1, 4, 8,15)( 2,10,12)( 3,14,11,13, 6, 5, 9, 7)
( 1,14,11, 3,13, 5,10, 2, 4,15)( 6, 9)( 7, 8)
( 1,13,10, 3, 6,11)( 2,12, 5, 8)( 7,15)
( 1, 2, 3,10, 6, 9, 7,12,11,13,14)( 4, 5, 8,15)
( 1, 3, 7,14, 5, 6)( 2, 9,12, 8, 4,11)(10,15,13)
( 1,13, 6, 8, 5, 9, 7)( 2,10,11,12,14)( 4,15)
( 1, 6, 5, 9)( 2, 7,13, 8,12, 3,10,11,15)
( 1, 8)( 2, 4,11, 6, 3, 7,14)( 5,12)( 9,10,13)

(Here is a screenshot http://i.imgur.com/krx3Iau.png)

My questions are:
(1) Does the seed determine the sequence of random elements of a fixed
group?
(2) Is the seed always the same for a fixed group?
(3) How can one change the seed?

Best,
Kieran.