Year: 2026
Type: article
Abstract: Cayley’s theorem tells us that all groups $$\textbf{G}$$ G occur as subgroups of the group of permutations over some set X . In this paper we consider a ‘sort-of’ converse to this question: given a set X and some transformation group $$\textbf{S}$$ S over X , what are the possible group structures on X that result in groups represented by $$\textbf{S}$$ S ? We solve this problem in the more general setting of faithful semigroups and observe that the solutions to this problem, which we term unrepresentations , have an inherent group structure. We study this phenomenon in depth before finishing with an analysis of the special case of unrepresentations of Clifford semigroups.
Source: Semigroup Forum
Authors: Peter F. Faul, Zurab Janelidze, Gideo Joubert
Institution: Stellenbosch University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
Funder: Universiteit Stellenbosch
OpenAlex ID: W7135196821