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This article defines a group property: a property that can be evaluated to true/false for any given group
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Definition

A group G is termed a n-Engel group if, for any , there exists n such that:

where the y occurs n times.

A group that is n-Engel for some positive integer n, is termed a bounded Engel group.

Relation with other properties

Weaker properties

• Engel group
• Nilpotent group: In fact a group of nilpotency class c is a c-Engel group.