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math.GR2022★ 2 cited
Abelianness and centrality in inverse semigroups
Michael Kinyon, David Stanovský
We adapt the abstract concepts of abelianness and centrality of universal algebra to the context of inverse semigroups. We characterize abelian and central congruences in terms of…
math.GR2022
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…
math.GR2022
Three concepts of nilpotence in loops
Žaneta Semanišinová, David Stanovský
We introduce the abstract concept of supernilpotence in loop theory, and relate it to existing concepts, namely, central nilpotence and nilpotence of the multiplication group. We p…