H,K are normal subgroups of a (finite) group G, and K is also normal in H. If G/K and G/H are simple, does it follow that H=K?(adsbygoogle = window.adsbygoogle || []).push({});

I'm almost convinced it does, but I'm having trouble proving it. I mean, the cosets of H partition G and the cosets of K partition G in the same way and on top of that partition H, right? I'm not sure when to bring in normality and the fact that the quotients are simple.

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

Dismiss Notice

Join Physics Forums Today!

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

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

# Normal and Simple groups

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