On locally graded $n$-Engel and positively $n$-Engel groups
Copyright policy )On locally graded $n$-Engel and positively $n$-Engel groups
Summary: We discuss four problems concerning \(n\)-Engel and so called positively \(n\)-Engel groups. As the answer to one of them we prove that in the class of locally graded groups every positively \(n\)-Engel group is locally nilpotent, which extends a similar result of \textit{D. M. Riley} [J. Group Theory 4, No. 4, 457-462 (2001; Zbl 1008.20031)] for residually finite groups.
positive laws, Engel conditions, local nilpotence, \(n\)-Engel groups, locally nilpotent groups, residually finite groups, locally graded groups, Local properties of groups, Residual properties and generalizations; residually finite groups, Quasivarieties and varieties of groups
positive laws, Engel conditions, local nilpotence, \(n\)-Engel groups, locally nilpotent groups, residually finite groups, locally graded groups, Local properties of groups, Residual properties and generalizations; residually finite groups, Quasivarieties and varieties of groups
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