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Abstract Given a group-word w and a group G, the verbal subgroup w ( G ) is the one generated by all w-values in G. The word w is said… Click to show full abstract
Abstract Given a group-word w and a group G, the verbal subgroup w ( G ) is the one generated by all w-values in G. The word w is said to be boundedly concise if for each positive integer m there exists a number depending only on m and w bounding the order of w ( G ) whenever the set of w-values in a group G has size at most m. In the present article we show that various generalizations of the Engel word are boundedly concise in residually finite groups.
Keywords:
bounded conciseness;
residually finite;
finite groups;
engel like;
like words;
conciseness engel
Journal Title: Journal of Algebra
Year Published: 2019
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Journal Title: Journal of Algebra
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!