---
tag: 6P42GTB2X6
kind: concept
name: Binary cyclic group
sources:
  - wikipedia: en:14423377@r1222211015
    locator: Binary cyclic group
    note: adopted
    mention: wikipedia://en/14423377
    sections: [Summary]
same_as:
  wikidata: Q2790210
  wikipedia: Binary cyclic group
inventory: [V7R5NMDM3S]
---

## Summary

In mathematics, the **binary cyclic group** of the *n*-gon is the cyclic group of order 2*n*, $C_{2n}$, thought of as an extension of the cyclic group $C_n$ by a [[cyclic group|0B85Q41RP6]] of order 2. Coxeter writes the *binary cyclic group* with angle-brackets, ⟨*n*⟩, and the index 2 subgroup as (*n*) or \[*n*\]<sup>\+</sup>.