Definition:Coset Product

Definition

Let $\struct {G, \circ}$ be a group.

Let $N$ be a normal subgroup of $G$.

Let $a, b \in G$.

The coset product of $a \circ N$ and $b \circ N$ is defined as the binary operation on the left coset space $G / N$ defined as:

$\paren {a \circ N} \circ \paren {b \circ N} = \paren {a \circ b} \circ N$

where $a \circ N$ and $b \circ N$ are the left cosets of $a$ and $b$ by $N$.

Also see

• Coset Product is Well-Defined
• Coset Product of Normal Subgroup is Consistent with Subset Product Definition

• Results about coset product can be found here.

Sources

• 1965: J.A. Green: Sets and Groups ... (previous) ... (next): $\S 6.7$. Quotient groups
• 1966: Richard A. Dean: Elements of Abstract Algebra ... (previous) ... (next): $\S 1.10$
• 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 50.2$ Quotient groups