Let G be a non-Abelian group such that |G| < 15 with proper subgroups H and...

 

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Let G be a non-Abelian group such that |G| < 15 with proper subgroups H and K such that G = H x K. Prove that G is isomorphic to Dg. I understand that the two subgroups must be H = {e,r3} and K = {e,r2,"4, f,r2f,raf} in Dg. I also know that Dg has order 12 but I do not understand why the less than or equal to 15 is necessary. I'm really not understanding why this must be always isomorphic to Do no matter the G. Let G be a non-Abelian group such that |G| < 15 with proper subgroups H and K such that G = H x K. Prove that G is isomorphic to Dg. I understand that the two subgroups must be H = {e,r3} and K = {e,r2,"4, f,r2f,raf} in Dg. I also know that Dg has order 12 but I do not understand why the less than or equal to 15 is necessary. I'm really not understanding why this must be always isomorphic to Do no matter the G.

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Solm et G be a nonAbeliam group Such that with prop... View the full answer