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forum.matefbc.ro • Vezi subiect - Actiuni ale morfismelor pe grupuri

Actiuni ale morfismelor pe grupuri

Algebra clasa a12a

Actiuni ale morfismelor pe grupuri

Mesajde Theodor Munteanu » Joi Mar 04, 2010 1:32 pm

1)Fie G un grup abelian si .Atunci urmatoarele afirmatii sunt echivalente:
a)
b) si
2)Se considera ecuatia functionala .
a)Sa se arate ca functia e injectiva si f(1)=1;
b)Daca ecuatia are solutii atunci G e comutativ;
c)Daca G e si finit atunci .
3)Fie un grup G cu proprietatea ca exista n natural astfel incat sunt morfisme .
Daca f e surjectiva atunci G e abelian.
Theodor Munteanu
 
Mesaje: 18
Membru din: Sâm Iun 27, 2009 3:45 pm

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