Ronald Biggers writes in his e-mail message of 1993/03/24 gap> z2 := Group( (1,2) );; gap> z2.name := "z2";; gap> g4 := Group( (1,3)(2,4), (1,2)(3,4) );; gap> g4.name := "g4";; gap> i4 := IdentityMapping( g4 );; gap> g8 := WreathProduct(z2, g4, i4);; gap> gt1 := Subgroup( g8, [ > WreathProductElement( (1,2), (), (), (), (), () ), > WreathProductElement( (), (1,2), (), (), (), () ), > WreathProductElement( (), (), (1,2), (), (), () ) ] );; gap> gt1.name := "gt1";; gap> x1 := Set( RightCosets( g8, gt1 ) );; gap> Operation( g8, x1, OnRightCosets ); Error, for: <list> must evaluate to a list at
Once upon a time right cosets weren't domains in GAP. They were simply
proper sets (i.e., sorted lists). 'OnRightCosets' then was the function
to use for those sets. That is 'OnRightCosets' takes a proper set,
multiplies all its elements with <g>, sorts the resulting list, and
returns this as the result.
Of course representing right cosets as lists was a stupid idea,
especially if the subgroup was large (or even infinite). Thus we changed
this (between GAP 3.0 and 3.1), so that right cosets are now domains. To
find the ``image'' of a right coset <C> under an element <g> you can now
write '<C> * <g>'. Thus you should use 'OnRight' instead of
gap> Operation( g8, x1, OnRight ); Group( (4,8), (3,7), (2,6), (1,5), (1,3)(2,4)(5,7)(6,8), (1,2)(3,4)(5,6)(7,8) )
Note that GAP 3.2 is a little bit more clever. If both <G> and <H> are
permutation groups, then 'WreathProduct( <G>, <H>, <alpha> )' will
automatically be represented as a permutation group.
gap> g8 := WreatProduct( z2, g4, i4 ); Group( (1,2), (3,4), (5,6), (7,8), (1,5)(2,6)(3,7)(4,8), (1,3)(2,4)(5,7)(6,8) )
So you don't have to go through 'gt1' and 'x1' to compute a permutation
representation any more. On the other hand if you still want to define
'gt1' you now have to specify it as 'Subgroup(g8,[(1,2),(3,4),(5,6)])'.
-- .- .-. - .. -. .-.. --- ...- . ... .- -. -. .. -.- .- Martin Sch"onert, Martin.Schoenert@Math.RWTH-Aachen.DE, +49 241 804551 Lehrstuhl D f"ur Mathematik, Templergraben 64, RWTH, D 51 Aachen, Germany