# Definition:Order of Structure/Finite Structure

Jump to navigation
Jump to search

## Definition

Let $\struct {S, \circ}$ be an algebraic structure.

Let the underlying set $S$ of $\struct {S, \circ}$ be finite.

Then $\struct {S, \circ}$ a **finite structure**.

That is, $\struct {S, \circ}$ is a **finite structure** if and only if $\struct {S, \circ}$ is not an infinite structure.

## Also known as

A **finite structure** can also be described as an algebraic structure **of finite order**.

## Also see

## Sources

- 1965: J.A. Green:
*Sets and Groups*... (previous) ... (next): $\S 4.4$. Gruppoids, semigroups and groups

This page may be the result of a refactoring operation.As such, the following source works, along with any process flow, will need to be reviewed. When this has been completed, the citation of that source work (if it is appropriate that it stay on this page) is to be placed above this message, into the usual chronological ordering.In particular: Determine whether "infinite structure" and/or "finite structure" are defined withinIf you have access to any of these works, then you are invited to review this list, and make any necessary corrections.To discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{SourceReview}}` from the code. |

- 1974: Thomas W. Hungerford:
*Algebra*... (previous) ... (next): $\text{I}$: Groups: $\S 1$ Semigroups, Monoids and Groups