Question

Hello, how can i do an isomorphism between group of order 6 and the S3 group?

Answer 1

Hoot! You just asked your first question! Hang tight while I find people to answer it for you. You can thank people who give you good answers by clicking the 'Good Answer' button on the right!

Answer 2

just visit chemistry group and before u go plz click the good answer button on the right

Answer 3

?? I'm talking about abstract algebra, in particular group theory.

Answer 4

what group of order 6 are you starting with

Answer 5

if it is cyclic or abelian there is no isomorphism

Answer 6

and every nonabelian group of order 6 should be isomorphic to S3

Answer 7

It doesn't matter; just take any non-anbelian group of order 6 and try to find the isomorphism.

And rsvitale i think you're wrong, cause if you take an abelian group it is isomorphic to \[Z _{3} or Z _{3} xZ _{2} \]

Answer 8

Excuse me \[Z _{6}\]

Answer 9

if there is an isomorphism from G --> G' then if G is abelian G' is abelian

Answer 10

and Z2xZ3 is isomorphic to Z6 since 2 and 3 are coprime

Answer 11

Exactly, but i want to know when the group is no abelian; i know that is isomophic to the permutation group S3 but i need to do the isomorphism.

Answer 12

ok do you want to send the symmetries of the regular triangle to the permutation group and show the two are isomorphic?

Answer 13

theres not really anything to do in that case, but I don't know what else to do the general non abelian group of order 6 is just S3 as far as I know. symmetries of a triangle is another way to show the permutation group

Answer 14

\[\phi(e)=e', \phi(\rho)=(123), etc..\]

Answer 15

the kernel is trivial so it is one to one, and phi(G)=G' so it is onto