On compact engel groups
Copyright policy )On compact engel groups
A group is called Engel if every two elements \(a,b\) of the group satisfy a relation of the form \[ [\cdots[[a,b],b],\dots,b]=1, \] where \([a,b]=a^{-1}b^{-1}ab\). In 1992, \textit{J. S. Wilson} and \textit{E. I. Zelmanov} [J. Pure Appl. Algebra 81, No. 1, 103-109 (1992; Zbl 0851.17007)] proved that a profinite Engel group is locally nilpotent. The author of the paper extends this result to all compact groups. As a corollary it is deduced that a compact group is locally nilpotent if and only if each of its two-generated subgroups is nilpotent.
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Engel groups, Engel conditions, Generalizations of solvable and nilpotent groups, Associated Lie structures for groups, Periodic groups; locally finite groups, locally nilpotent groups, compact groups, Limits, profinite groups, Compact groups, pro-\(p\) groups, Local properties of groups
Engel groups, Engel conditions, Generalizations of solvable and nilpotent groups, Associated Lie structures for groups, Periodic groups; locally finite groups, locally nilpotent groups, compact groups, Limits, profinite groups, Compact groups, pro-\(p\) groups, Local properties of groups
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