Visual Group Theory, Lecture 3.5: Quotient groups

Visual Group Theory, Lecture 3.5: Quotient groups Like how a direct product can be thought of as a way to "multiply" two groups, a quotient is a way to "divide" a group by one of its subgroups. We start by defining this in terms of collapsing Cayley diagrams, until we get a conjecture about what property a subgroup H needs to have for the quotient G/H to exist. At this point, we translate everything into formal algebraic language and prove this theorem. Specifically, the quotient exists when the set of left cosets of H forms a group. This requires a well-defined binary operation, which exists if and only if H is a normal subgroup. Course webpage (with lecture notes, HW, etc.): http://www.math.clemson.edu/~macaule/...