How Are Cosets Related to Normal Subgroups?

[walwaldoggy]

Hey guys
I'm curious about how to interpret cosets and normal subgroups.
I do know the definitions of both, but I do not understand how they relate to each other.
A (left) coset is supposed to partition a group as well as normal subgroups, but I'm sure there is a more profound relationship between the two than just the similarity I have pointed out.

I'll look forward to your inputs!

 

[micromass]

I'm not sure what you're looking for. A normal subgroup is simply a subgroup who's left cosets are also right cosets. Also the cosets of a normal subgroup form a group themself: the quotient group.

There are certainly nice relationships between cosets and normal subgroups, but I'm not certain which ones you want. Maybe you can clarify?

Also, I'm not quite sure what you mean with "normal subgroups partition the group"...