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,