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@nskeip
Last active November 11, 2020 07:29
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Верно ли что если Н' нормальна в G, то H нормальна в G?
# Верно ли что если Н' нормальна в G, то H нормальна в G?
# Нет. Приведем пример, когда H' нормальна в G, но H не нормальна в G
# полезное: IsNormal, DerivedSubgroup
# https://alex-konovalov.github.io/ukrgap/gapbook/chapC.html#X87D263A4841FD6A1
for n in [3..10] do
G := SymmetricGroup(n);
Print("Checking ", n, "\n");
for ccs in ConjugacyClassesSubgroups(G) do
H := Representative(ccs);
dH := DerivedSubgroup(H);
if not IsTrivial(dH) and IsNormal(G, dH) and not IsNormal(G, H) then
Print(G, "; H: ", H, "; H': ", dH, "\n");
fi;
od;
od;
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