I read in a book on groups and representations that any transitive [tex]G[/tex]-set is isomorphic to the coset space of some subgroup of [tex]G[/tex].(adsbygoogle = window.adsbygoogle || []).push({});

Does this mean we can determine all transitive [tex]G[/tex]-sets up to isomorphism simply by finding all subgroups of [tex]G[/tex]?

Just want to make sure that if this is the case that I have in my mind the right idea, so we take [tex]G = S_3[/tex], then all transitive [tex]G[/tex]-sets are up to isomorphism...

[tex]G / \{e\}, G / \langle (12) \rangle , G / \langle (132) \rangle , G / G[/tex]?

Note I do realize that [tex]\langle (13) \rangle[/tex] is also a subgroup of [tex]S_3[/tex] but the way I see it the coset space would be the same as [tex]G / \langle (12) \rangle[/tex]

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Isomorphic G sets

Loading...

**Physics Forums | Science Articles, Homework Help, Discussion**