cyclic group

循环群

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

Translation evidence: Literature usage

Meaning in context

A group generated by one element, so every element is an integer power of that generator.

可由单个元素生成、每个元素均为其整数次幂的群。

Example

Z/7Z\mathbb Z/7\mathbb Z is generated additively by 1ˉ\bar1.

Usage and distinctions

Cyclic groups may be infinite; cyclic does not mean finite.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Wen-Wei Li — Methods in Algebra I, author source半群, 幺半群与群 (sec:group-and-monoid), definition def:cyclic-group (循环群) · Checked 2026-10-15

Translation sources

  1. 李文威 — 代数学方法 卷一，作者源文件半群, 幺半群与群 (sec:group-and-monoid), definition def:cyclic-group (循环群) · Checked 2026-10-15
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