Definition:Cayley Table/Also known as

Cayley Table: Also known as

Some sources refer to a Cayley table as an operation table, but there exists the view that this sounds too much like a piece of hospital apparatus.

Another popular name for this is a multiplication table, but this holdover from grade school terminology may be considered irrelevant to a table where the operation has nothing to do with multiplication as such.

In the field of logic, a truth table in this format is often referred to as matrix form, but note that this terminology clashes with the definition of a matrix in mathematics.

Sources

• 1951: Nathan Jacobson: Lectures in Abstract Algebra: Volume $\text { I }$: Basic Concepts ... (previous) ... (next): Chapter $\text{I}$: Semi-Groups and Groups: $1$: Definition and examples of semigroups
• 1964: W.E. Deskins: Abstract Algebra ... (previous) ... (next): $\S 1.4$
• 1964: Walter Ledermann: Introduction to the Theory of Finite Groups (5th ed.) ... (previous) ... (next): Chapter $\text {I}$: The Group Concept: $\S 5$: The Multiplication Table
• 1965: J.A. Green: Sets and Groups ... (previous) ... (next): $\S 4.1$. Binary operations on a set: Example $58$
• 1967: George McCarty: Topology: An Introduction with Application to Topological Groups ... (previous) ... (next): Chapter $\text{II}$: Groups: Exercise $\text{A}$
• 1982: P.M. Cohn: Algebra Volume 1 (2nd ed.) ... (previous) ... (next): $\S 3.2$: Groups; the axioms: Examples of groups $\text{(v)}$
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Cayley table