Showing Subgroups of a Permutation Group are Isomorphicby Obraz35 Tags: group theory, isomorphic, isomorphism, permutations 

#1
Mar509, 05:25 PM

P: 31

Define two subgroups of S6:
G=[e, (123), (123)(456)] H=[e, (14), (123)(456)] Determine whether G and H are isomorphic. It seems as if they should be since they have the same cardinality and you can certainly map the elements to one another, but I don't know what other factors need to be considered when deciding whether they are isomorphic. 



#2
Mar509, 05:30 PM

P: 13

H is not a subgroup since (14)(123)(456) = (123456) which is not in H. Are you sure you've written down the correct group?




#3
Mar509, 09:09 PM

P: 31

Oops. I meant G=<(123), (123)(456)> and H=<(14), (123)(456)>.



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