Definition:Symmetric Group/Notation

Definition

In order not to make notation for operations on a symmetric group overly cumbersome, product notation is usually used for mapping composition.

Thus $\pi \circ \rho$ is written $\pi \rho$.

Also, for the same reason, rather than using $I_{S_n}$ for the identity mapping, the symbol $e$ is usually used.

Sources

• 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 34$. Examples of groups: $(4) \ \text {(b)}$