Thread: Abstract Algebra - Cosets

Yup thanks. I had one of my professors explain it to me. Forgot to post up. Thanks though! :)

Originally Posted by vwishndaetr H is a subset. Where h is an element of the set H. Right. So, what does it mean for the set aH to be equal to the set bH? Oh, and you can type the "in" symbol using a "\in" and the "not in" symbol using "otin". I think it formats it better that way.

First of all, you need to say "H is a subgroup of G " or the problem doesn't make sense. Now, what is the definition of "aH" and "bH"? Your remark that "I wanted to say that it is only true when a=b" indicates that you are not clear on that definition.

Remember that aH and bH partition the group (since they are equivalence classes defined by a=b if b = ah for some h in H), if you had any two cosets which had a nonzero intersection, then the transitivity of equivalence classes would automatically make the two equal. So to begin with, you know that if c is in aH, then c equals ah for h in H. if d is in bH, it equals d = bh', for h' in H. Your condition for the equivalence classes...