REVIEW 1 cited by
On commutative set-theoretic solutions of the Pentagon Equation
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
read the original abstract
We extend the so-called retract relation given in [6] for involutive set-theoretic solutions of the Pentagon Equation and we introduce the notion of associated permutation group to study the family of the commutative non-degenerate ones. Moreover, we develop a machinery to construct all these solutions and we use it to give a quite explicit classification of the irretractable ones. Finally, non-degenerate solutions on left-zero semigroup are studied in detail, with an emphasis on the ones with cyclic associated permutation group and on the ones having small size.
Forward citations
Cited by 1 Pith paper
-
Associative Pentagon Algebras
Associative pentagon algebras are classified into left- and right-trivially distributive families, characterized respectively by the semigroup varieties VP2 and VQ1.
Discussion (0). Sign in to comment.