Groups satisfying semigroup laws, and nilpotent-by-Burnside varieties

DOI10.1006/JABR.1997.7088zbMath0886.20022OpenAlexW2017354109MaRDI QIDQ1372662

Robert G. Burns, Olga Macedońska, Yuri A. Medvedev

Publication date: 3 March 1998

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jabr.1997.7088

zbMATH Keywords

finitely generated groupsresidually finite groupsproducts of varietiesfinite bases of identitiessemigroup lawsnilpotent varietiesnilpotent-by-finite exponent groupsrestricted Burnside varieties

Mathematics Subject Classification ID

Generalizations of solvable and nilpotent groups (20F19) Residual properties and generalizations; residually finite groups (20E26) Quasivarieties and varieties of groups (20E10) Local properties of groups (20E25)

Related Items (25)

On Positive Law Problems in the Class of Locally Graded Groups ⋮ Which Words have an Efficient Result? ⋮ On locally finite 𝑝-groups satisfying an Engel condition ⋮ On groups satisfying a positive law in fixed points. ⋮ Milnor Property in Finitely Generated Soluble Groups ⋮ On some classes of orderable groups ⋮ Bounds for nilpotent-by-finite groups in certain varieties ⋮ GB-Problem in the Class of Locally Graded Groups ⋮ How to Tell if a Group Law Entails Virtual Nilpotence: Postscript ⋮ Growth of unbounded sets in nilpotent groups and random mapping statistics ⋮ Positive laws in fixed points of automorphisms of finite groups. ⋮ Which words spell ``almost nilpotent? ⋮ What do the Engel laws and positive laws have in common? ⋮ Words and Almost Nilpotent Varieties of Groups^# ⋮ On laws of the form \(ab\equiv ba\) equivalent to the abelian law ⋮ Polynomial growth in semigroup varieties. ⋮ On non-Hopfian groups of fractions ⋮ Positive laws on word values in residually-\(p\) groups. ⋮ Groups with a positive law on commutators. ⋮ Engel-like conditions in fixed points of automorphisms of profinite groups ⋮ Positive laws in fixed points ⋮ Group Laws Implying Virtual Nilpotence ⋮ Milnor's alternative for finitely generated relatively free groups that are locally graded ⋮ Collapsing groups and positive laws ⋮ Two questions on semigroup laws

Cites Work

• New estimates of odd exponents of infinite Burnside groups.
• Powerful \(p\)-groups. I: Finite groups.
• Groups of polynomial growth and expanding maps. Appendix by Jacques Tits
• Combinatorial conditions in residually finite groups. I
• Combinatorial conditions in residually finite groups. II
• On almost fixed point free automorphisms
• On periodic compact groups
• Growth of finitely generated solvable groups
• Growth of finitely generated solvable groups and curvature of Riemannian manifolds
• ON SOME PROBLEMS OF GROUP THEORY AND LIE ALGEBRAS
• On the Finiteness of Certain Soluble Groups
• SOLUTION OF THE RESTRICTED BURNSIDE PROBLEM FOR GROUPS OF ODD EXPONENT
• Two-Generator conditions for Residually Finite Groups
• Milnor identities
• Laws in Nilpotent-by-Finite Groups
• Varieties of soluble groups and a dichotomy of P. Hall
• Subsemigroups of nilpotent groups
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