What does "cyclic group" mean?

A group generated by a single element.

Cyclic group

Q: What is a synonym for "cyclic group"?

Common synonyms include: abelian group, abelian structure, commutative group, cyclical, generator group, group of one generator.

noun

noun ·Rare ·Advanced level

Definitions

Noun

1
A group generated by a single element.
"1986, N. S. Gopalakrishnan, University Algebra, New Age International, 2nd Edition, page 22, Proposition 1.5.6. Any subgroup of an infinite cyclic group is also an infinite cyclic group."

Synonyms

All synonyms

abelian group abelian structure commutative group cyclical generator group group of one generator

Antonyms

All antonyms

acyclic aperiodic klein nonabelian group

Example

More examples

"1986, N. S. Gopalakrishnan, University Algebra, New Age International, 2nd Edition, page 22, Proposition 1.5.6. Any subgroup of an infinite cyclic group is also an infinite cyclic group."

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