# Cyclic group

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Abelian group - Wikipedia, the free encyclopedia

In organic chemistry, the phenyl group or phenyl ring is a cyclic group of atoms with the formula C6H5. Phenyl groups are closely related to benzene. Phenyl groups have six carbon atoms bonded together in a hexagonal planar ring, five of which are bonded to individual hydrogen atoms, with the remaining carbon bonded to a substituent.

Proof that Z x Z is not a cyclic group

Proof that (R, +) is not a Cyclic Group

Every Cyclic Group is Abelian Proof

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

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

Examples of Cyclic Groups

Direct Products of Finite Cyclic Groups Video 1

The cyclic group Z26 underlies Caesar's cipher.