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# System prepended metadata

title: Cyclic Group 定義
tags: [crypto]

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---
title: Cyclic Group 定義
tags: crypto
lang: zh_tw
---

* [筆記總覽](https://hackmd.io/@LJP/rkerFdnqS)

[TOC]

# Cyclic Group 定義
A group $(G,\ \bullet)$ is **cyclic** if there exists a **generator** $g\in G$ such that every $a\in G$ is of the form $a=g\ \bullet\ ...\ \bullet\ g\ (n\ \mathrm{copies})$ for some $n\in Z$

## 例子
- $(Z,\ +)$ is cyclic with generators 1 and -1