Thanks. I am sorry for some stupid questions (for e.g. Q1)

Let me plz state what all I have understood and you can correct it if I am wrong.

1) H is a normal sub-group IF AND ONLY IF every right coset of H, is a left coset of H as well.

2) If H is not a normal sub-group then there is

**atleast one **right coset of H which is not a left coset of H

(I have an unrelated confusion here - if there is

**one **right coset which is not a left coset, does this imply there is

**atleast one **left coset which is not a right coset. Or these two condition are not related?)

3)

=> Ha = Hb; but not aH = bH

Sorry if I am getting confused un-necessarily plz.