Transversal (Group Theory)/Examples/Integer Multiples in Integers

Example of Transversal in the Context of Group Theory

Let $\struct {\Z, +}$ denote the additive group of integers.

Let $\struct {n \Z, +}$ denote the additive group of integer multiples.

Then a transversal for $\struct {n \Z, +}$ in $\struct {\Z, +}$ is:

$\set {0, 1, \ldots, n - 1}$

Sources

• 1965: J.A. Green: Sets and Groups ... (previous) ... (next): $\S 6.3$. Index. Transversals: Example $116$