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character of a finite group (Definition)
Definition 1   Let $ G$ be a finite group, and let $ K$ be a field. A character from $ G$ to $ K$ is a group homomorphism $ \chi\colon G\to K^\times$, where $ K^\times$ is the multiplicative group $ K\setminus\{0_K\}$.

Example: The Dirichlet characters are characters from $ \mathbb{Z}/m\mathbb{Z}$ to $ \mathbb{C}$.



"character of a finite group" is owned by alozano.
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See Also: Dirichlet character

Other names:  character

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the sum of the values of a character of a finite group is $0$ (Theorem) by alozano
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Cross-references: Dirichlet characters, multiplicative group, group homomorphism, field, finite group
There are 31 references to this entry.

This is version 3 of character of a finite group, born on 2004-02-20, modified 2005-04-25.
Object id is 5600, canonical name is CharacterOfAFiniteGroup.
Accessed 4882 times total.

Classification:
AMS MSC: 11A25 (Number theory :: Elementary number theory :: Arithmetic functions; related numbers; inversion formulas)
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