gap> InputLogTo("newfunction");
InputLogTo: cannot log to newfunction at
INPUT_LOG_TO( name );
 called from
<function>( <arguments> ) called from read-eval-loop
Entering break read-eval-print loop ...
you can 'quit;' to quit to outer loop, or
you can 'return;' to continue
brk> gap> InputLogTo("newest");
InputLogTo: cannot log to newest at
INPUT_LOG_TO( name );
 called from
<function>( <arguments> ) called from read-eval-loop
Entering break read-eval-print loop ...
you can 'quit;' to quit to outer loop, or
you can 'return;' to continue
brk> gap> quit;
gap> newfunction(6);
Variable: 'newfunction' must have a value

gap> Read("newfunction");
gap> Read("newfunction");
gap> newfunction(6);
4
gap> newfunction(11);
4
gap> Read("newfunction2");
gap> newfunction2(6);
1
gap> Read("oops");
Error, file "oops" must exist and be readable called from
<function>( <arguments> ) called from read-eval-loop
Entering break read-eval-print loop ...
you can 'quit;' to quit to outer loop, or
you can 'return;' to continue
brk> gap> G1 := SymmetricGroup(8);
Sym( [ 1 .. 8 ] )
gap> f1 := (1,2,3,4)(5,6,7,8);
(1,2,3,4)(5,6,7,8)
gap> l1 := (1,5,6,2)(4,8,7,3);
(1,5,6,2)(3,4,8,7)
gap> K1 := Subgroup(G1,[f1,l1]);
Group([ (1,2,3,4)(5,6,7,8), (1,5,6,2)(3,4,8,7) ])
gap> Size(K1);
24
gap> G2 := SymmetricGroup(6);
Sym( [ 1 .. 6 ] )
gap> f2 := (1,5,6,3);
(1,5,6,3)
gap> l2 := (1,4,6,2);
(1,4,6,2)
gap> K2 := Subgroup(G2,[f2,l2]);
Group([ (1,5,6,3), (1,4,6,2) ])
gap> Size(K2);
24
gap> IsomorphismGroups(K1,K2);
[ (1,2,3,4)(5,6,7,8), (1,5,6,2)(3,4,8,7) ] -> [ (1,3,6,5), (2,3,4,5) ]
gap> f:=FreeGroup(2);
<free group on the generators [ f1, f2 ]>
gap> G:=f/[f.1^3,f.2^9,f.1^2*f.2*f.1*f.2];
<fp group on the generators [ f1, f2 ]>
gap> f.1;
f1
gap> f.2;
f2
gap> Size(3);
Error, no method found! For debugging hints type ?Recovery from NoMethodFound
Error, no 1st choice method found for `Size' on 1 arguments called from
<function>( <arguments> ) called from read-eval-loop
Entering break read-eval-print loop ...
you can 'quit;' to quit to outer loop, or
you can 'return;' to continue
brk> gap> Size(G);
3
gap> Order(f.1);
user interrupt at
MakeImmutable( a );
 called from
Inverse( obj ) called from
<function>( <arguments> ) called from read-eval-loop
Entering break read-eval-print loop ...
you can 'quit;' to quit to outer loop, or
you can return to continue
brk> gap> g.1;
Variable: 'g' must have a value

gap> Order(g.1);
Variable: 'g' must have a value

gap> Order(G.1);
3
gap> f:=FreeGroup("a","b");
<free group on the generators [ a, b ]>
gap> x:=f.1; y:=f.2;
a
b
gap> rels:=[x^2,y^3,(x*y)^5];
[ a^2, b^3, a*b*a*b*a*b*a*b*a*b ]
gap> G:=f/rels;
<fp group on the generators [ a, b ]>
gap> Size(G);
60
gap> A:=AlternatingGroup(5);
Alt( [ 1 .. 5 ] )
gap> IsomorphismGroups(G,A);
[ b*a*b^2*a*b*a*b^2, a*b*a*b*a*b^2 ] -> [ (1,4)(2,5), (1,2,3) ]
gap> IsomorphismGroups(A,G);
[ (1,4)(2,5), (1,2,3) ] -> [ b*a*b^2*a*b*a*b^2, a*b*a*b*a*b^2 ]
gap> f:=FreeGroup("a","b");
<free group on the generators [ a, b ]>
gap> x:=f.1; y:=f.2;
a
b
gap> rels:=[x^5,y^2,x^-1*y^-1*x^2*y];
[ a^5, b^2, a^-1*b^-1*a^2*b ]
gap> G:=f/rels;
<fp group on the generators [ a, b ]>
gap> Size(G);
2
gap> f:=FreeGroup("a","b");
<free group on the generators [ a, b ]>
gap> f:=FreeGroup("a","b");
<free group on the generators [ a, b ]>
gap> x:=f.1; y:=f.2;
a
b
gap> rels:=[x^6,y^3,y^-1*x*y*x^3];
[ a^6, b^3, b^-1*a*b*a^3 ]
gap> G:=f/rels;
<fp group on the generators [ a, b ]>
gap> Size(G);
6
gap> IsAbelian(G);
true
gap> f:=FreeGroup("a","b","c","d");
<free group on the generators [ a, b, c, d ]>
gap> x:=f.1; y:=f.2; z:=f.3; w:=f.4;
a
b
c
d
gap> rels:=[x*y*z^-1,y*z*w^-1,z*w*x^-1,w*x*y^-1];
[ a*b*c^-1, b*c*d^-1, c*d*a^-1, d*a*b^-1 ]
gap> G:=f/rels;
<fp group on the generators [ a, b, c, d ]>
gap> Size(G);
5
gap> f:=FreeGroup("a","b");
<free group on the generators [ a, b ]>
gap> x:=f.1; y:=f.2;
a
b
gap> rels:=[x^3,y^3,(x*y)^2];
[ a^3, b^3, a*b*a*b ]
gap> G:=f/rels;
<fp group on the generators [ a, b ]>
gap> Size(G);
12
gap> IsAbelian(G);
false
gap> Elements(G);
[ <identity ...>, a, a^2, a*b, b, a^2*b, a*b*a, a^2*b*a, b*a, a*b*a^2, b*a^2, a^2*b*a^2 ]
gap> List(Elements(G),x->Order(x));
[ 1, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 2 ]
gap> A:=AlternatingGroup(4);
Alt( [ 1 .. 4 ] )
gap> List(Elements(A),x->Order(x));
[ 1, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 2 ]
gap> NumberSmallGroups(12);
5
gap> List(AllSmallGroups(12),x->List(Elements(x),y->Order(y)));
[ [ 1, 4, 2, 3, 4, 4, 6, 3, 4, 4, 6, 4 ], [ 1, 4, 3, 2, 12, 4, 3, 6, 12, 12, 6, 12 ], [ 1, 3, 2, 2, 3, 3, 3, 2, 3, 3, 3, 3 ], 
  [ 1, 2, 2, 3, 2, 2, 6, 3, 2, 2, 6, 2 ], [ 1, 2, 2, 3, 2, 6, 6, 3, 6, 6, 6, 6 ] ]
gap> f:=FreeGroup("a","b");
<free group on the generators [ a, b ]>
gap> x:=f.1; y:=f.2;
a
b
gap> rels:=[x^3,y^2];
[ a^3, b^2 ]
gap> G:=f/rels;
<fp group on the generators [ a, b ]>
gap> Size(G);
#I  Coset table calculation failed -- trying with bigger table limit
#I  Coset table calculation failed -- trying with bigger table limit
#I  Coset table calculation failed -- trying with bigger table limit
user interrupt at
app[11] := firstDef;
 called from
TCENUM.CosetTableFromGensAndRels( fgens, grels, fsgens ) called from
CosetTableFromGensAndRels( fgens, grels, List( trial, UnderlyingElement ) ) called from
Attempt( trial ) called from
Attempt( gens ) called from
FinIndexCyclicSubgroupGenerator( G, infinity ) called from
...
Entering break read-eval-print loop ...
you can 'quit;' to quit to outer loop, or
you can return to continue
brk> #I  Options stack has been reset
gap> LowIndexSubgroupsFpGroup(G,TrivialSubgroup(G),6);
[ Group(<fp, no generators known>), Group(<fp, no generators known>), Group(<fp, no generators known>), 
  Group(<fp, no generators known>), Group(<fp, no generators known>), Group(<fp, no generators known>), 
  Group(<fp, no generators known>), Group(<fp, no generators known>), Group(<fp, no generators known>), 
  Group(<fp, no generators known>), Group(<fp, no generators known>), Group(<fp, no generators known>), 
  Group(<fp, no generators known>), Group(<fp, no generators known>), Group(<fp, no generators known>) ]
gap> LogTo();