5 Five families

5.4 Symmetric and alternating groups

5.4.4 Cayley’s theorem

The author’s footnote regarding composition is a bit unfortunate. It’s fine and good to choose this particular convention: it’s also the choice of GAP, Permutations - SymPy and Permutations · AbstractAlgebra.jl. However, these libraries don’t necessarily use ∘ (“ring operator” in Unicode) for composition.

Per Function composition § Alternative notations, the more common notational preference is \(f∘g\) for “g then f” although it gives mention to the author’s convention. We’ll prefer \(f⨟g\) for “f then g” when it doesn’t conflict with the author.