Words of Engel type are concise in residually finite groups
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 concise if w(G) is finite whenever the set of w-values in G is finite. In 1960s, Hall asked whether every word is concise but later Ivanov answered this question in the ne...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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World Scientific Publishing
2019-08-01
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| Series: | Bulletin of Mathematical Sciences |
| Subjects: | |
| Online Access: | http://www.worldscientific.com/doi/pdf/10.1142/S1664360719500127 |
| Summary: | 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 concise if w(G) is finite whenever the set of w-values in G is finite. In 1960s, Hall asked whether every word is concise but later Ivanov answered this question in the negative. On the other hand, Hall’s question remains wide open in the class of residually finite groups. In the present paper we show that various generalizations of the Engel word are concise in residually finite groups. |
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| ISSN: | 1664-3607 1664-3615 |