On Engel-like congruences
Paul M. Weichsel (1974)
Compositio Mathematica
Richard E. Phillips, J. M. Plotkin (1975)
Colloquium Mathematicae
Budkin, A.I., Taranina, L.V. (2000)
Siberian Mathematical Journal
Mikaelian, Vahagn H. (2004)
Beiträge zur Algebra und Geometrie
Ralph Strebel (1981)
Commentarii mathematici Helvetici
Ján Jakubík (1985)
Mathematica Slovaca
Almeida, J., Delgado, M. (2001)
Portugaliae Mathematica. Nova Série
Almeida, J., Delgado, M. (1999)
Portugaliae Mathematica
S.V. Ivanov (1994)
Semigroup forum
Timoshenko, E.I. (2000)
Siberian Mathematical Journal
B. Bajorska, O. Macedońska (2001)
Colloquium Mathematicae
Let G* denote a nonprincipal ultrapower of a group G. In 1986 M.~Boffa posed a question equivalent to the following one: if G does not satisfy a positive law, does G* contain a free nonabelian subsemigroup? We give the affirmative answer to this question in the large class of groups containing all residually finite and all soluble groups, in fact, all groups considered in traditional textbooks on group theory.
Timoshenko, E.I. (2002)
Sibirskij Matematicheskij Zhurnal
Pride, S.J. (1985)
Publications de l'Institut Mathématique. Nouvelle Série
Timoshenko, E.I. (2001)
Sibirskij Matematicheskij Zhurnal
L. Polák (1987)
Semigroup forum
Libor Polák (1988)
Semigroup forum
Gérard Lallement, Elaine Milito (1975)
Semigroup forum
Tomas Everaert, Marino Gran (2006)
Archivum Mathematicum
In this note we determine explicit formulas for the relative commutator of groups with respect to the subvarieties of -nilpotent groups and of -solvable groups. In particular these formulas give a characterization of the extensions of groups that are central relatively to these subvarieties.
Sidney A. Morris (1974)
Matematický časopis
Michael W. Thomson (1979)
Mathematische Zeitschrift