The algorithms that recognize Milnor laws and properties of these laws
We consider several equivalent definitions of the so-called Milnor laws (or Milnor identities) that is the laws which are not satisfied in ApA varieties. The purpose of this article is to provide algorithms that allow us to check whether a given identity w(x, y) has one of the following properties:...
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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2014 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут прикладної математики і механіки НАН України
2014
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/153340 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | The algorithms that recognize Milnor laws and properties of these laws / W. Tomaszewski // Algebra and Discrete Mathematics. — 2014. — Vol. 17, № 2. — С. 308–332. — Бібліогр.: 38 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862644572029452288 |
|---|---|
| author | Tomaszewski, W. |
| author_facet | Tomaszewski, W. |
| citation_txt | The algorithms that recognize Milnor laws and properties of these laws / W. Tomaszewski // Algebra and Discrete Mathematics. — 2014. — Vol. 17, № 2. — С. 308–332. — Бібліогр.: 38 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | We consider several equivalent definitions of the so-called Milnor laws (or Milnor identities) that is the laws which are not satisfied in ApA varieties. The purpose of this article is to provide algorithms that allow us to check whether a given identity w(x, y) has one of the following properties: w(x, y) is a Milnor law, every nilpotent group satisfying w(x, y) is abelian, every finitely generated metabelian group satisfying w(x, y) is finite-by-abelian.
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| first_indexed | 2025-12-01T09:31:44Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-153340 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-01T09:31:44Z |
| publishDate | 2014 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Tomaszewski, W. 2019-06-14T03:24:13Z 2019-06-14T03:24:13Z 2014 The algorithms that recognize Milnor laws and properties of these laws / W. Tomaszewski // Algebra and Discrete Mathematics. — 2014. — Vol. 17, № 2. — С. 308–332. — Бібліогр.: 38 назв. — англ. 1726-3255 2010 MSC:20E10, 20F16. https://nasplib.isofts.kiev.ua/handle/123456789/153340 We consider several equivalent definitions of the so-called Milnor laws (or Milnor identities) that is the laws which are not satisfied in ApA varieties. The purpose of this article is to provide algorithms that allow us to check whether a given identity w(x, y) has one of the following properties: w(x, y) is a Milnor law, every nilpotent group satisfying w(x, y) is abelian, every finitely generated metabelian group satisfying w(x, y) is finite-by-abelian. The author wishes to thank Olga Macedońska for many helpful remarks and valuable suggestions. The author also thanks Janusz Słupikfor reviewing and improving the computer program which is the implementation of algorithms. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics The algorithms that recognize Milnor laws and properties of these laws Article published earlier |
| spellingShingle | The algorithms that recognize Milnor laws and properties of these laws Tomaszewski, W. |
| title | The algorithms that recognize Milnor laws and properties of these laws |
| title_full | The algorithms that recognize Milnor laws and properties of these laws |
| title_fullStr | The algorithms that recognize Milnor laws and properties of these laws |
| title_full_unstemmed | The algorithms that recognize Milnor laws and properties of these laws |
| title_short | The algorithms that recognize Milnor laws and properties of these laws |
| title_sort | algorithms that recognize milnor laws and properties of these laws |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/153340 |
| work_keys_str_mv | AT tomaszewskiw thealgorithmsthatrecognizemilnorlawsandpropertiesoftheselaws AT tomaszewskiw algorithmsthatrecognizemilnorlawsandpropertiesoftheselaws |