linear representation of a finite group

有限群的线性表示

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Translation evidence: Literature usage

Meaning in context

A homomorphism $\rho:G\to\operatorname{GL}(V)$ for a finite group $G$ and an $F$-vector space $V$.

由有限群到某域上向量空间的一般线性群的群同态。

Example

$S_3$ permutes coordinates of $F^3$.

Usage and distinctions

Complete reducibility is guaranteed by Maschke only when the characteristic does not divide $|G|$.

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Definition sources

1. J. S. Milne — Group TheoryChapter 7, Linear representations and Maschke's theorem · Checked 2026-10-14

Translation sources

1. 中国科学院数学与系统科学研究院暑期学校 — 群表示论讲义（HFUT 教学页所链接）§1, 有限群的表示, definition of a representation · Checked 2026-10-14

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