Definition:Group Endomorphism
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Definition
Let $\struct {G, \circ}$ be a group.
Let $\phi: G \to G$ be a (group) homomorphism from $G$ to itself.
Then $\phi$ is a group endomorphism.
Also see
- Results about group endomorphisms can be found here.
Linguistic Note
The word endomorphism derives from the Greek morphe (μορφή) meaning form or structure, with the prefix endo- (from ἔνδον') meaning inner or internal.
Thus endomorphism means internal structure.
Sources
- 1965: J.A. Green: Sets and Groups ... (previous) ... (next): $\S 7.1$. Homomorphisms
- 1966: Richard A. Dean: Elements of Abstract Algebra ... (previous) ... (next): $\S 1.10$
- 1970: B. Hartley and T.O. Hawkes: Rings, Modules and Linear Algebra ... (previous) ... (next): Chapter $1$: Rings - Definitions and Examples: $2$: Some examples of rings: Ring Example $10$
- 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Chapter $2$: Group Homomorphism and Isomorphism: $\S 60$
- 1982: P.M. Cohn: Algebra Volume 1 (2nd ed.) ... (previous) ... (next): $\S 3.2$: Groups; the axioms