Groups%2C Algorithms and Programming, aka Groups, Algorithms and Programming, is an actively used programming language created in 1986. GAP (Groups, Algorithms and Programming) is a computer algebra system for computational discrete algebra with particular emphasis on computational group theory.. Read more on Wikipedia...

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Example code from Linguist:

gap> START_TEST("Test of factor groups and natural homomorphisms");

gap> G:=HeisenbergPcpGroup(2);
Pcp-group with orders [ 0, 0, 0, 0, 0 ]

gap> H:=Subgroup(G,[G.2,G.3,G.4,G.5]);
gap> K:=G/H;
gap> NaturalHomomorphism(K);

gap> A:=Subgroup(H, [G.3]);
Pcp-group with orders [ 0 ]
gap> B:=Subgroup(Subgroup(G,[G.1,G.4,G.5]), [G.4]);
Pcp-group with orders [ 0 ]
gap> Normalizer(A,B);
Pcp-group with orders [ 0 ]
gap> # The following used to trigger the error "arguments must have a common parent group"
gap> Normalizer(B,A);
Pcp-group with orders [ 0 ]

gap> STOP_TEST( "factor.tst", 10000000);

Example code from Wikipedia:

gap> G:=SmallGroup(8,1); # Set G to be a group of order 8.
<pc group of size 8 with 3 generators>
gap> i:=IsomorphismPermGroup(G); # Find an isomorphism from G to a group of permutations
<action isomorphism>
gap> Image(i,G); # The image of G under I - these are the generators of im G.
Group([ (1,5,3,7,2,6,4,8), (1,3,2,4)(5,7,6,8), (1,2)(3,4)(5,6)(7,8) ])
gap> Elements(Image(i,G)); # All the elements of im G.
[ (), (1,2)(3,4)(5,6)(7,8), (1,3,2,4)(5,7,6,8), (1,4,2,3)(5,8,6,7), 
   (1,5,3,7,2,6,4,8), (1,6,3,8,2,5,4,7), (1,7,4,5,2,8,3,6), (1,8,4,6,2,7,3,5) ]

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Last updated August 9th, 2020

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