On automorphism groups of a biplane (121,16,2)
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866909128850407424 |
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| author | Crnković, Dean Danilović, Doris Dumičić Rukavina, Sanja |
| author_facet | Crnković, Dean Danilović, Doris Dumičić Rukavina, Sanja |
| contents | The existence of a biplane with parameters $(121,16,2)$ is an open problem. Recently, it has been proved by Alavi, Daneshkhah and Praeger that the order of an automorphism group of a of possible biplane ${\mathcal D}$ of order $14$ divides $2^7\cdot3^2\cdot5\cdot7\cdot11\cdot13$. In this paper we show that such a biplane do not have an automorphism of order $11$ or $13$, and thereby establish that $|Aut({\mathcal D})|$ divides $2^7\cdot3^2\cdot5\cdot7.$ Further, we study a possible action of an automorphism of order five or seven, and some small groups of order divisible by five or seven, on a biplane with parameters $(121,16,2)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_12944 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | On automorphism groups of a biplane (121,16,2) Crnković, Dean Danilović, Doris Dumičić Rukavina, Sanja Combinatorics 05B05, 20B25 The existence of a biplane with parameters $(121,16,2)$ is an open problem. Recently, it has been proved by Alavi, Daneshkhah and Praeger that the order of an automorphism group of a of possible biplane ${\mathcal D}$ of order $14$ divides $2^7\cdot3^2\cdot5\cdot7\cdot11\cdot13$. In this paper we show that such a biplane do not have an automorphism of order $11$ or $13$, and thereby establish that $|Aut({\mathcal D})|$ divides $2^7\cdot3^2\cdot5\cdot7.$ Further, we study a possible action of an automorphism of order five or seven, and some small groups of order divisible by five or seven, on a biplane with parameters $(121,16,2)$. |
| title | On automorphism groups of a biplane (121,16,2) |
| topic | Combinatorics 05B05, 20B25 |
| url | https://arxiv.org/abs/2010.12944 |