The Existence of Triple Factorizations for Sporadic Groups of Rank 3
A finite group G with proper subgroups A and B has triple factorization G = ABA if every element g of G can be represented as g = aba0 , where a and a 0 are from A and b is from B. Such a triple factorization may be sometimes degenerate to AB-factorization. The task of finding triple factorizations...
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| Format: | Article |
| Language: | English |
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Yaroslavl State University
2015-04-01
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| Series: | Моделирование и анализ информационных систем |
| Subjects: | |
| Online Access: | https://www.mais-journal.ru/jour/article/view/242 |
| _version_ | 1826558993275813888 |
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| author | L. S. Kazarin I. A. Rassadin D. N. Sakharov |
| author_facet | L. S. Kazarin I. A. Rassadin D. N. Sakharov |
| author_sort | L. S. Kazarin |
| collection | DOAJ |
| description | A finite group G with proper subgroups A and B has triple factorization G = ABA if every element g of G can be represented as g = aba0 , where a and a 0 are from A and b is from B. Such a triple factorization may be sometimes degenerate to AB-factorization. The task of finding triple factorizations for a group is fundamental and can be used for understanding the group structure. For instance, every simple finite group of Lie type has a natural factorization of such a type. Besides, the triple factorization is widely used in the study of graphs, geometries and varieties. The goal of this article is to find triple factorizations for sporadic groups of rank 3. We have proved the existence theorem of ABA-factorization for sporadic simple groups McL and F i22. There exist two rank 3 permutation representations of F i22. We have proved that ABA-factorizations exist in both cases. |
| first_indexed | 2024-04-10T02:25:24Z |
| format | Article |
| id | doaj.art-d819a1787959432992ec7c640f511ec2 |
| institution | Directory Open Access Journal |
| issn | 1818-1015 2313-5417 |
| language | English |
| last_indexed | 2025-03-14T08:53:19Z |
| publishDate | 2015-04-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj.art-d819a1787959432992ec7c640f511ec22025-03-02T12:46:57ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172015-04-0122221923710.18255/1818-1015-2015-2-219-237235The Existence of Triple Factorizations for Sporadic Groups of Rank 3L. S. Kazarin0I. A. Rassadin1D. N. Sakharov2P.G. Demidov Yaroslavl State UniversityООО «Нетис Телеком»ООО «Агентство развития «4Р»A finite group G with proper subgroups A and B has triple factorization G = ABA if every element g of G can be represented as g = aba0 , where a and a 0 are from A and b is from B. Such a triple factorization may be sometimes degenerate to AB-factorization. The task of finding triple factorizations for a group is fundamental and can be used for understanding the group structure. For instance, every simple finite group of Lie type has a natural factorization of such a type. Besides, the triple factorization is widely used in the study of graphs, geometries and varieties. The goal of this article is to find triple factorizations for sporadic groups of rank 3. We have proved the existence theorem of ABA-factorization for sporadic simple groups McL and F i22. There exist two rank 3 permutation representations of F i22. We have proved that ABA-factorizations exist in both cases.https://www.mais-journal.ru/jour/article/view/242group factorizationsporadic groupsmclaughlin groupfisher group |
| spellingShingle | L. S. Kazarin I. A. Rassadin D. N. Sakharov The Existence of Triple Factorizations for Sporadic Groups of Rank 3 Моделирование и анализ информационных систем group factorization sporadic groups mclaughlin group fisher group |
| title | The Existence of Triple Factorizations for Sporadic Groups of Rank 3 |
| title_full | The Existence of Triple Factorizations for Sporadic Groups of Rank 3 |
| title_fullStr | The Existence of Triple Factorizations for Sporadic Groups of Rank 3 |
| title_full_unstemmed | The Existence of Triple Factorizations for Sporadic Groups of Rank 3 |
| title_short | The Existence of Triple Factorizations for Sporadic Groups of Rank 3 |
| title_sort | existence of triple factorizations for sporadic groups of rank 3 |
| topic | group factorization sporadic groups mclaughlin group fisher group |
| url | https://www.mais-journal.ru/jour/article/view/242 |
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