Automorphism Group of a Possible 2-(121, 16, 2) Symmetric Design
Let D be a symmetric 2-(121, 16, 2) design with the automorphism group of Aut(D). In this paper the order of automorphism of prime order of Aut(D) is studied, and some results are obtained about the number of fixed points of these automorphisms. Also we will show that |Aut(D)|=2p 3q 5r 7s 11t 13u, w...
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| Format: | Article |
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| Language: | English |
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University of Tehran
2009-03-01
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| Series: | Journal of Sciences, Islamic Republic of Iran |
| Online Access: | https://jsciences.ut.ac.ir/article_31914_d27e9d8cefd3b17f8206cb7ff8128cc7.pdf |
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| collection | DOAJ |
| description | Let D be a symmetric 2-(121, 16, 2) design with the automorphism group of Aut(D). In this paper the order of automorphism of prime order of Aut(D) is studied, and some results are obtained about the number of fixed points of these automorphisms. Also we will show that |Aut(D)|=2p 3q 5r 7s 11t 13u, where p, q, r, s, t and u are non-negative integers such that r, s, t, u ? 1. In addition we present some general results on the automorphisms with prime order of a symmetric design and some general results on the automorphism groups of a symmetric design are given and in Section 3, we prove a series of Lemma. Based on them we can prove main Theorem. One of the reasons for the emergence and growth of block designs is the combined irrigation of fields having a lot of patches, at the end of the paper, there is offered an application of block design in modern irrigation. |
| format | Article |
| id | doaj-art-cf009a06f00b45479976db7c35e13b95 |
| institution | OA Journals |
| issn | 1016-1104 2345-6914 |
| language | English |
| publishDate | 2009-03-01 |
| publisher | University of Tehran |
| record_format | Article |
| series | Journal of Sciences, Islamic Republic of Iran |
| spelling | doaj-art-cf009a06f00b45479976db7c35e13b952025-08-20T02:25:52ZengUniversity of TehranJournal of Sciences, Islamic Republic of Iran1016-11042345-69142009-03-0120131914Automorphism Group of a Possible 2-(121, 16, 2) Symmetric DesignLet D be a symmetric 2-(121, 16, 2) design with the automorphism group of Aut(D). In this paper the order of automorphism of prime order of Aut(D) is studied, and some results are obtained about the number of fixed points of these automorphisms. Also we will show that |Aut(D)|=2p 3q 5r 7s 11t 13u, where p, q, r, s, t and u are non-negative integers such that r, s, t, u ? 1. In addition we present some general results on the automorphisms with prime order of a symmetric design and some general results on the automorphism groups of a symmetric design are given and in Section 3, we prove a series of Lemma. Based on them we can prove main Theorem. One of the reasons for the emergence and growth of block designs is the combined irrigation of fields having a lot of patches, at the end of the paper, there is offered an application of block design in modern irrigation.https://jsciences.ut.ac.ir/article_31914_d27e9d8cefd3b17f8206cb7ff8128cc7.pdf |
| spellingShingle | Automorphism Group of a Possible 2-(121, 16, 2) Symmetric Design Journal of Sciences, Islamic Republic of Iran |
| title | Automorphism Group of a Possible 2-(121, 16, 2) Symmetric Design |
| title_full | Automorphism Group of a Possible 2-(121, 16, 2) Symmetric Design |
| title_fullStr | Automorphism Group of a Possible 2-(121, 16, 2) Symmetric Design |
| title_full_unstemmed | Automorphism Group of a Possible 2-(121, 16, 2) Symmetric Design |
| title_short | Automorphism Group of a Possible 2-(121, 16, 2) Symmetric Design |
| title_sort | automorphism group of a possible 2 121 16 2 symmetric design |
| url | https://jsciences.ut.ac.ir/article_31914_d27e9d8cefd3b17f8206cb7ff8128cc7.pdf |