Group Laws Implying Virtual Nilpotence

DOI10.1017/S1446788700003335zbMath1066.20030OpenAlexW2098569041MaRDI QIDQ4462470

Robert G. Burns, Yuri A. Medvedev

Publication date: 18 May 2004

Published in: Journal of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s1446788700003335

zbMATH Keywords

subgroups of finite indexnilpotent groupslocally graded groupsmetabelian groupsgroup lawsEngel lawsmonoidal laws

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) Engel conditions (20F45)

Related Items

On the commuting probability for subgroups of a finite group ⋮ How to Tell if a Group Law Entails Virtual Nilpotence: Postscript ⋮ Bounding the order of a verbal subgroup in a residually finite group ⋮ On compact Engel groups. ⋮ What do the Engel laws and positive laws have in common? ⋮ Words and Almost Nilpotent Varieties of Groups^# ⋮ POSITIVE LAWS ON LARGE SETS OF GENERATORS: COUNTEREXAMPLES FOR INFINITELY GENERATED GROUPS ⋮ On laws of the form \(ab\equiv ba\) equivalent to the abelian law ⋮ On bounded conciseness of Engel-like words in residually finite groups ⋮ On finiteness of some verbal subgroups in profinite groups ⋮ Positive laws on word values in residually-\(p\) groups. ⋮ On generalization of minimal non-nilpotent groups. ⋮ Strong conciseness in profinite groups ⋮ On Finite Number of Conjugacy Classes in Groups ⋮ Words of Engel type are concise in residually finite groups

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• Milnor identities
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• Invariant Measures and Growth Conditions
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