Sylow subgroup

Sylow 子群

Algebra & Algebraic Geometry · Undergraduate · Mathematics Resources editorial compilation (AI-assisted)

Translation evidence: Literature usage

Meaning in context

For a finite group of order $p^am$ with prime $p$ and $p\nmid m$, a subgroup of order $p^a$.

有限群的阶为 $p^am$ 且 $p\nmid m$ 时，阶为 $p^a$ 的子群。

Example

A subgroup generated by a transposition is a Sylow $2$-subgroup of $S_3$.

Usage and distinctions

A maximal $p$-power divisor of the group order is required, not any $p$-subgroup.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

1. Wen-Wei Li — Methods in Algebra I, author sourceSylow 定理 (sec:Sylow), definition immediately after the p^a || n convention following Cauchy's theorem (prop:group-Cauchy), naming Sylow p-子群 by its order p^m · Checked 2026-10-15

Translation sources

1. 李文威 — 代数学方法 卷一，作者源文件Sylow 定理 (sec:Sylow), definition immediately after the p^a || n convention following Cauchy's theorem (prop:group-Cauchy), naming Sylow p-子群 by its order p^m · Checked 2026-10-15

Original encyclopedia and terminology content: CC BY-SA 4.0. Contribute or report a correction.