Semigroup theory of symmetry

Vladimir R. Rosenfeld, Thomas E Nordahl

Research output: Contribution to journalLetterpeer-review

3 Scopus citations


Symmetry is one of the most fundamental concepts of all nature. We discuss the general theory of symmetry based on theory of semigroups. This includes and extends the theory of groups, which is by now broadly used as an algebraic tool for studying many types of symmetries observed by people. However, symmetry groups are only a particular case of more general, symmetry semigroups. The latter are in turn an instance of an even more general groupoids of symmetry, which may further be a topic of special consideration.

Original languageEnglish (US)
Pages (from-to)1758-1776
Number of pages19
JournalJournal of Mathematical Chemistry
Issue number9
StatePublished - Oct 1 2016


  • Automorphism (symmetry) group
  • Color symmetry
  • Endomorphism monoid
  • Fractal
  • Hidden regularities
  • Hidden symmetry
  • Inverse semigroup
  • Monoid
  • Orbit
  • Quasicrystal
  • Semifractal
  • Semigroup

ASJC Scopus subject areas

  • Chemistry(all)
  • Applied Mathematics


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