Associative words in the symmetric group of degree three
Let G be a group. An element \(w(x,y)\) of the absolutely free group on free generators \(x,y\) is called an associative word in \(G\) if the equality \(w(w(g_1,g_2),g_3)=w(g_1,w(g_2,g_3))\) holds for all \(g_1,g_2 \in G\). In this paper we determine all associative words in the symmetric group on...
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| Date: | 2018 |
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| Main Author: | |
| Format: | Article |
| 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/736 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543270038929408 |
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| author | Plonka, Ernest |
| author_facet | Plonka, Ernest |
| author_sort | Plonka, Ernest |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-04-26T00:47:27Z |
| description | Let G be a group. An element \(w(x,y)\) of the absolutely free group on free generators \(x,y\) is called an associative word in \(G\) if the equality \(w(w(g_1,g_2),g_3)=w(g_1,w(g_2,g_3))\) holds for all \(g_1,g_2 \in G\). In this paper we determine all associative words in the symmetric group on three letters. |
| first_indexed | 2026-02-08T08:00:33Z |
| format | Article |
| id | admjournalluguniveduua-article-736 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T08:00:33Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-7362018-04-26T00:47:27Z Associative words in the symmetric group of degree three Plonka, Ernest associative words, symmetric group \(S_3\) 20B30, 08A40,20F12 Let G be a group. An element \(w(x,y)\) of the absolutely free group on free generators \(x,y\) is called an associative word in \(G\) if the equality \(w(w(g_1,g_2),g_3)=w(g_1,w(g_2,g_3))\) holds for all \(g_1,g_2 \in G\). In this paper we determine all associative words in the symmetric group on three letters. Lugansk National Taras Shevchenko University 2018-04-26 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/736 Algebra and Discrete Mathematics; Vol 15, No 1 (2013) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/736/267 Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | associative words symmetric group \(S_3\) 20B30 08A40,20F12 Plonka, Ernest Associative words in the symmetric group of degree three |
| title | Associative words in the symmetric group of degree three |
| title_full | Associative words in the symmetric group of degree three |
| title_fullStr | Associative words in the symmetric group of degree three |
| title_full_unstemmed | Associative words in the symmetric group of degree three |
| title_short | Associative words in the symmetric group of degree three |
| title_sort | associative words in the symmetric group of degree three |
| topic | associative words symmetric group \(S_3\) 20B30 08A40,20F12 |
| topic_facet | associative words symmetric group \(S_3\) 20B30 08A40,20F12 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/736 |
| work_keys_str_mv | AT plonkaernest associativewordsinthesymmetricgroupofdegreethree |