# Mappings to Algebraic Structure form Similar Algebraic Structure

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It has been suggested that this page or section be merged into Definition:Induced Structure.In particular: This has I believe been documented elsewhere and more rigorously. Merging probably needed, or just deletion.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 `{{Mergeto}}` from the code. |

## Theorem

Let $X$ be a nonempty set.

Let $G$ be a magma with respect to the binary operations $\circ_1, \ldots, \circ_n$ on $G$.

Let $G^X$ be the set of all mappings from $X$ to $G$.

Denote also by $\circ_1, \ldots, \circ_n$ the binary operations defined on $G^X$ by pointwise addition.

Work In ProgressIn particular: Transcluded pages for group, monoid, abelian group, and so on, and so forthYou can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by completing it.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 `{{WIP}}` from the code. |

## Also see

## Sources

- 1974: Thomas W. Hungerford:
*Algebra*... (previous) ... (next): $\text{I}$: Groups: $\S 1$: Semigroups, Monoids and Groups: Exercise $2$