File: morpheus.tst

package info (click to toggle)
gap 4r4p12-2
  • links: PTS
  • area: main
  • in suites: squeeze, wheezy
  • size: 29,584 kB
  • ctags: 7,113
  • sloc: ansic: 98,786; sh: 3,299; perl: 2,263; makefile: 498; asm: 63; awk: 6
file content (78 lines) | stat: -rw-r--r-- 1,985 bytes parent folder | download | duplicates (3)
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
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
#############################################################################
##
#W  morpheus.tst                GAP tests                    Alexander Hulpke
##
#H  @(#)$Id: morpheus.tst,v 4.18.2.4 2005/08/29 14:50:35 gap Exp $
##
#Y  Copyright (C)  1997,  Lehrstuhl D fuer Mathematik,  RWTH Aachen,  Germany
##
##  This  file  tests the automorphism routines
##
##  To be listed in testall.g
##

gap> START_TEST("$Id: morpheus.tst,v 4.18.2.4 2005/08/29 14:50:35 gap Exp $");

gap> g:=Group((1,2,3,4),(1,3));;
gap> a:=AutomorphismGroup(g);;
gap> inn:=InnerAutomorphismsAutomorphismGroup(a);;
gap> iso1:=IsomorphismGroups(a,g);;
gap> iso1=fail;
false
gap> iso2:=IsomorphismGroups(g,a);;
gap> iso2=fail;
false
gap> iso3:=iso2*iso1;;
gap> if not iso3 in inn then iso3:=iso3*iso3;fi;
gap> r:=RepresentativeAction(g,GeneratorsOfGroup(g),
>           List(GeneratorsOfGroup(g),i->Image(iso3,i)),OnTuples);;
gap> r=fail;
false
gap> iso4:=iso3*InnerAutomorphism(g,r^-1);;
gap> iso4=IdentityMapping(g);
true

gap> g:=TransitiveGroup(6,7);;
gap> IsSolvableGroup(g);
true
gap> Size(AutomorphismGroup(g));
24

gap> g:=Group((1,2,3),(1,2));;
gap> g:=Image(IsomorphismPcGroup(DirectProduct(g,g,g,g)));;
gap> Size(g);
1296
gap> Size(AutomorphismGroup(g))/Size(g);
24

gap> g:=Group((1,2,3),(4,5,6),(7,8),(9,10),(11,12,13,14,15));
Group([ (1,2,3), (4,5,6), (7,8), (9,10), (11,12,13,14,15) ])
gap> a:=AutomorphismGroup(g);;
gap> Size(a);
1152
gap> Size(DerivedSubgroup(a));
72
gap> p:=IsomorphismPcGroup(a);;
gap> Image(p,a.1);;
gap> Image(p,a.1*a.2);;
gap> Pcgs(a);;
gap> s4 := Group( (3,4), (1,2,3,4) );;
gap> d8 := Subgroup( s4, [ (1,2)(3,4), (1,2,3,4) ] );;
gap> autd8 := AutomorphismGroup( d8 );;
gap> Size(autd8);
8
gap> DisplayCompositionSeries(AutomorphismGroup(SymmetricGroup(3)));
G (size 6)
 | Z(2)
S (1 gens, size 3)
 | Z(3)
1 (size 1)

# that's all, folks
gap> STOP_TEST( "morpheus.tst", 557400000 );


#############################################################################
##
#E