14 citations · 28 across the 21 of their papers we have counts for
30 papers
Supernilpotent groups and -supernilpotent loops
David Stanovský, Petr Vojtěchovský
We find a short equational basis for the variety of -supernilpotent loops. We also present a conceptually simple proof that -nilpotence and -supernilpotence are equivalent…
Idempotent solutions of the Yang-Baxter equation and twisted group division
David Stanovský, Petr Vojtěchovský
Idempotent left nondegenerate solutions of the Yang-Baxter equation are in one-to-one correspondence with twisted Ward left quasigroups, which are left quasigroups satisfying the i…
Subdirect products and propagating equations with an application to Moufang theorem
Aleš Drápal, Petr Vojtěchovský
We introduce the concept of propagating equations and focus on the case of associativity propagating in varieties of loops. An equation propagates in an algebra i…
Enumeration of involutory latin quandles, Bruck loops and commutative automorphic loops of odd prime power order
Izabella Stuhl, Petr Vojtěchovský
There is a one-to-one correspondence between involutory latin quandles and uniquely -divisible Bruck loops. Bruck loops of odd prime power order are centrally nilpotent. Using l…
Bol loops and Bruck loops of order up to isotopism
Petr Vojtěchovský
Let be odd primes. We classify Bol loops and Bruck loops of order up to isotopism. When does not divide , the only Bol loop (and hence the only Bruck loop) of…
Set-theoretic Yang-Baxter (co)homology theory of involutive non-degenerate solutions
Józef H. Przytycki, Petr Vojtěchovský, Seung Yeop Yang
W. Rump showed that there exists a one-to-one correspondence between involutive right non-degenerate solutions of the Yang-Baxter equation and Rump right quasigroups. J. S. Carter,…