"Source: Text/Group/GrpCoh.text";
"Line: 768";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/GrpCoh.text, line: 768
// Example: H75E12 ()
print "Example: H75E12";
ei := GetEchoInput();
SetEchoInput(true);
G := GL(3, 2);                                                        
M := GModule(G);
H := Sylow(G, 2);
CG := CohomologyModule(G, M); 
CH := Restriction(CG, H);
H1G := CohomologyGroup(CG, 1); H1G;
H1H := CohomologyGroup(CH, 1); H1H;
res1 := hom<H1G -> H1H | x:->IdentifyOneCocycle(CH,OneCocycle(CG,x)) >;
res1(H1G.1);
H2G := CohomologyGroup(CG, 2); H2G;
H2H := CohomologyGroup(CH, 2); H2H;
res2 := hom<H2G -> H2H | x:-> IdentifyTwoCocycle(CH,TwoCocycle(CG,x)) >;
res2(H2G.1);                                                       
H:=sub< G | G.2, G.2^(G.1*G.2*G.1) >;
#H;
assert $1 eq 21;
CH := Restriction(CG, H);
CohomologyGroup(CH, 1); CohomologyGroup(CH, 2);
t:=TwoCocycle(CG,[1]);
isc, o := IsTwoCoboundary(CH, t);
isc;
assert $1;
forall{ <h,k> : h in H, k in H | t(<h,k>) eq
           o(<h>)*MatrixOfElement(CH,k) + o(<k>) - o(<h*k>) };
assert $1;
SetEchoInput(ei);
