Forum Problem Lists Definitions FAQ

16.16 (2006)

Open

a) Does the set of (not necessarily boundedly) Engel elements of a group without elements of order 2 form a subgroup?
b) The same question for torsion-free groups.
c) The same question for right-ordered groups.
d) The same question for linearly ordered groups.

Contributor: V. V. Bludov

Progress

There are examples of 2-groups where a product of two (unboundedly) Engel elements is not an Engel element.

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