Phrase guide

cyclic group

noun · 1 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

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1

noun

Meaning 1

A group generated by a single element.

Definition source: English Wiktionary via Wiktextract

Topics: group-theory, mathematics, sciences

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.
  • 2003, Alexander Retakh (translator), Ėrnest Borisovich Vinberg, A Course in Algebra, [2001, Э. Б. Винберг, Курс алгебры, Factorial Press] American Mathematical Society, page 152, Cyclic groups are the simplest groups imaginable.

Meaning relationships

Synonyms: monogenous group

Antonyms: none provided

History

Etymology

No etymology was provided for this word.

Across languages

Translations

2 source translations are retained for this English entry.

  • Italian: gruppo ciclico — group generated by a single element
  • Polish: grupa cykliczna — group generated by a single element