Commutators, word maps and Engel conditions

Commutator calculus and nilpotency in (often infinite) groups: basic commutators, Engel elements, locally nilpotent and hypercentral groups, metabelian and polycyclic groups, localization of nilpotent groups, commutator width and length, word maps and their images, and local word identities.

• Basic commutators
• Commutator power identities
• Commutator width
• Engel conditions on involutions
• Engel elements
• Groups with unique ordered-product normal forms
• Intersection of the derived series
• Local word identities
• Localization of nilpotent groups
• Locally nilpotent groups
• Non-commutators in finite groups
• Perfect locally nilpotent p-groups
• Residually nilpotent groups
• Word maps on Lie groups

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