# Cyclic group

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Phenyl group - Wikipedia, the free encyclopedia

The circle of fifths may be endowed with a cyclic group structure

Examples of Cyclic Groups

Every Cyclic Group is Abelian Proof

In organic chemistry, the phenyl group or phenyl ring is a cyclic group of atoms with the formula C6H5.

The cyclic group Z26 underlies Caesar's cipher.

Cyclic Groups

Cyclic Group

A Cayley graph for the free product of the cyclic groups C3 and C5 (with the natural generating set). Drawn in TikZ :)

The largest mathematical proof in history is generally considered to be the classification of finite simple groups. The proof consists of tens of thousands of pages, published in several hundred journal articles, by about 100 authors, mostly between 1955 and 2004. It states that every finite simple group is isomorphic to one of the following groups: a cyclic group with prime order; an alternating group of degree at least five; a simple group of Lie type; the…