On verbal subgroups in finite and profinite groups
Let w be a multilinear commutator word. In the present paper we describe recent results that show that if G is a profinite group in which all w-values are contained in a union of finitely (or in some cases countably) many subgroups with a prescribed property, then the verbal subgroup w(G) has the sa...
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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2012 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2012
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/152224 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On verbal subgroups in finite and profinite groups / C. Acciarri, P. Shumyatsky // Algebra and Discrete Mathematics. — 2012. — Vol. 14, № 1. — С. 1–13. — Бібліогр.: 32 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | Let w be a multilinear commutator word. In the present paper we describe recent results that show that if G is a profinite group in which all w-values are contained in a union of finitely (or in some cases countably) many subgroups with a prescribed property, then the verbal subgroup w(G) has the same property as well. In particular, we show this in the case where the subgroups are periodic or of finite rank.
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| ISSN: | 1726-3255 |