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# unitlib, chapter 2
#
# DO NOT EDIT THIS FILE - EDIT EXAMPLES IN THE SOURCE INSTEAD!
#
# This file has been autogenerated with GAP. It contains examples
# extracted from the documentation. Each example is preceded by the
# comment which points to the location of its source.
#
gap> START_TEST( "unitlib02.tst");
# doc/funct.xml:61-66
gap> PcNormalizedUnitGroupSmallGroup(128,161);
<pc group of size 170141183460469231731687303715884105728 with 127 generators>
# doc/funct.xml:89-110
gap> V:=PcNormalizedUnitGroup(GroupRing(GF(2),SmallGroup(8,3)));
<pc group of size 128 with 7 generators>
gap> V1:=PcNormalizedUnitGroupSmallGroup(8,3);
<pc group of size 128 with 7 generators>
gap> V1=V; # two isomorphic groups but not identical objects
false
gap> IdGroup(V)=IdGroup(V1);
true
gap> IsomorphismGroups(V,V1);
[ f1, f2, f3, f4, f5, f6, f7 ] -> [ f1, f2, f3, f4, f5, f6, f7 ]
gap> KG:=UnderlyingGroupRing(V1); # now the correct way
<algebra-with-one over GF(2), with 3 generators>
gap> V1=PcNormalizedUnitGroup(KG); # V1 is an attribute of KG
true
gap> K:=UnderlyingField(KG);
GF(2)
gap> G:=UnderlyingGroup(KG);
<pc group of size 8 with 3 generators>
# doc/funct.xml:117-128
gap> f:=Embedding(G,V1);
[ f1, f2, f3 ] -> [ f1, f2, f4 ]
gap> g:=List(GeneratorsOfGroup(G), x -> x^f );
[ f1, f2, f4 ]
gap> G1:=Subgroup(V1,g);
Group([ f1, f2, f4 ])
gap> IdGroup(G1);
[ 8, 3 ]
# doc/funct.xml:207-223
gap> SavePcNormalizedUnitGroup( SmallGroup( 256, 56092 ) );
true
gap> PcNormalizedUnitGroupSmallGroup( 256, 56092 );
WARNING : the library of V(KG) for groups of order
256 is not available yet !!!
You can use only groups from the unitlib/userdata directory
in case if you already computed their descriptions
(See the manual for SavePcNormalizedUnitGroup).
#I Description of V(KG) for G=SmallGroup(256,
56092) accepted, started its generation...
<pc group of size
57896044618658097711785492504343953926634992332820282019728792003956564819968
with 255 generators>
gap> STOP_TEST("unitlib02.tst", 1 );
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