> < ^ Date: Tue, 11 Aug 1992 09:26:34 +0200
> < ^ From: Frank Celler <frank.celler@math.rwth-aachen.de >
< ^ Subject: Re: Permutation groups from Ag groups

Dear David,

DS> following is a summary of what I tried, but it doesn't work.
DS>
DS> gap> a:=TwoGroup(256,3678);;
DS> gap> b:=Subgroup(a,[a.1^2,a.2^2,a.3^2]);;
DS> gap> g:=Operation(a,Cosets(a,b),OnRightCosets);;
DS> Error, for: <list> must evaluate to a list at
DS> for <var> in set ... in
DS> opr( D[i], gen ) called from
DS> arg[1].operations.Operation( arg[1], arg[2], arg[3] ) called from
DS> Operation( a, Cosets( a, b ), OnRightCosets ) called from
DS> main loop

this is because the name 'OnRightCosets' is (unfortunately) misleading.
'OnRightCosets' expects a set \$S\$ and an element \$g\$ and returns \$Sg\$.
For cosets you should use 'OnRight'.

```gap> a := TwoGroup( 256, 3678 );
Group( a1, a2, a3, a4, a5, a6, a7, a8 )
gap> b := Subgroup( a, [a.1^2,a.2^2,a.3^2] );
Subgroup( Group( a1, a2, a3, a4, a5, a6, a7, a8 ), [ a4*a5*a6, a4*a5, a4 ] )
gap> g := Operation( a, Cosets(a,b), OnRight );
Group( ( 1,17)( 2,18)( 3,19)( 4,20)( 5,21, 8,24)( 6,22, 7,23)( 9,25,11,27)
(10,26,12,28)(13,29,14,30)(15,31,16,32), ( 1, 9)( 2,10)( 3,11)( 4,12)
( 5,13, 7,15)( 6,14, 8,16)(17,28,18,27)(19,26,20,25)(21,32,24,29)
(22,31,23,30), ( 1, 5)( 2, 6)( 3, 7)( 4, 8)( 9,16,10,15)(11,14,12,13)
(17,22,19,24)(18,21,20,23)(25,32,28,29)(26,31,27,30), ( 9,10)(11,12)(13,14)
(15,16)(17,19)(18,20)(21,23)(22,24)(25,28)(26,27)(29,32)(30,31), ( 5, 7)
( 6, 8)( 9,10)(11,12)(13,16)(14,15)(17,20)(18,19)(21,22)(23,24)(25,27)
(26,28), ( 5, 6)( 7, 8)( 9,11)(10,12)(13,16)(14,15)(17,18)(19,20)(25,28)
(26,27)(29,31)(30,32), ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,15)
(14,16)(17,19)(18,20)(21,23)(22,24)(25,27)(26,28)(29,31)(30,32), ( 1, 2)
( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)
(25,26)(27,28)(29,30)(31,32) )
```

DS> (BTW, is this forum broken? I have not received any messages in

We do have some problems with our list server.

mfg
Frank

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