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...
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| Date: | 2018 |
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| Language: | English |
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Lugansk National Taras Shevchenko University
2018
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/707 |
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| Journal Title: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-7072018-04-04T09:58:22Z On verbal subgroups in finite and profinite groups Acciarri, Cristina Shumyatsky, Pavel Profinite groups, verbal subgroups, coverings, multilinear commutators Primary 20E18; Secondary 20F14 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. Lugansk National Taras Shevchenko University 2018-04-04 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/707 Algebra and Discrete Mathematics; Vol 14, No 1 (2012) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/707/240 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
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| datestamp_date |
2018-04-04T09:58:22Z |
| collection |
OJS |
| language |
English |
| topic |
Profinite groups verbal subgroups coverings multilinear commutators Primary 20E18 Secondary 20F14 |
| spellingShingle |
Profinite groups verbal subgroups coverings multilinear commutators Primary 20E18 Secondary 20F14 Acciarri, Cristina Shumyatsky, Pavel On verbal subgroups in finite and profinite groups |
| topic_facet |
Profinite groups verbal subgroups coverings multilinear commutators Primary 20E18 Secondary 20F14 |
| format |
Article |
| author |
Acciarri, Cristina Shumyatsky, Pavel |
| author_facet |
Acciarri, Cristina Shumyatsky, Pavel |
| author_sort |
Acciarri, Cristina |
| title |
On verbal subgroups in finite and profinite groups |
| title_short |
On verbal subgroups in finite and profinite groups |
| title_full |
On verbal subgroups in finite and profinite groups |
| title_fullStr |
On verbal subgroups in finite and profinite groups |
| title_full_unstemmed |
On verbal subgroups in finite and profinite groups |
| title_sort |
on verbal subgroups in finite and profinite groups |
| description |
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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/707 |
| work_keys_str_mv |
AT acciarricristina onverbalsubgroupsinfiniteandprofinitegroups AT shumyatskypavel onverbalsubgroupsinfiniteandprofinitegroups |
| first_indexed |
2025-07-17T10:36:32Z |
| last_indexed |
2025-07-17T10:36:32Z |
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1837890108247769089 |