Yes this is a coset, its purpose or application is probably not that important at this stage.
I would make sure you understand how to find aH and Ha and the differences. (aH = Ha only when H is a normal subgroup of G)
Do you have an example?
What does it mean to multiply an element of a group by a subgroup?
From my Discrete class notes:
Let be a group (a set with an operation that is closed and associative, has an identity and every element has an inverse). Let be a subgroup of .
, define relation as if .
Relation is called a 'coset'.
What does that relation, coset, mean? I interpret the definition as " relation if left times a subgroup equals left times the same subgroup". But that is kind of meaningless. What is an element times a subgroup?
Thanks, in advance,
No example. I typed everything in my notes (and I'm listening to my recording of the lecture now, there is nothing more in what the Prof. said).
I guess my question was more along the lines of, what is a coset? What is ? Is it just multiplying times ? If yes, what does it mean to multiply an element by a set? Does that simply mean multiplying times every element of the set? If yes, doesn't that imply that the coset is not a subset of the subgroup.
The textbook does not have any information on cosets and I'm loathe to look at Wikipedia (it often confuses me worse).
P.S. What happens if I agree with you? (re: your signature)