On point-transitive and transitive deficiency one parallelisms of PG 详细信息    查看全文

• 作者：Svetlana Topalova ; Stela Zhelezova
• 关键词：Spread ; Parallelism ; Transitivity ; Automorphisms ; 05B05 ; 51E20 ; 51E23
• 刊名：Designs, Codes and Cryptography
• 出版年：2015
• 出版时间：April 2015
• 年：2015
• 卷：75
• 期：1
• 页码：9-19
• 全文大小：179 KB
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Combinatorics
  Coding and Information Theory
  Data Structures, Cryptology and Information Theory
  Data Encryption
  Discrete Mathematics in Computer Science
  Information, Communication and Circuits
  
• 出版者：Springer Netherlands
• ISSN：1573-7586

文摘

A parallelism in PG \((n,q)\) is point-transitive if it has an automorphism group which is transitive on the points. If the automorphism group fixes one spread and is transitive on the remaining spreads, the parallelism corresponds to a transitive deficiency one parallelism. It is known that there are three types of spreads in PG \((3,4)\) —regular, subregular and aregular. A parallelism is regular if all its spreads are regular. In PG \((3,4)\) no point-transitive parallelisms, no regular ones, and no transitive deficiency one parallelisms have been known. Both point-transitive parallelisms and transitive deficiency one parallelisms must have automorphisms of order 5. We construct all 32,048 nonisomorphic parallelisms with automorphisms of order 5 and classify them by the orders of their automorphism groups and by the types of their spreads. There are 31,832 parallelisms with an automorphism group fixing exactly one spread. Only for four of them the automorphism group is transitive on the remaining spreads. Among the parallelisms we construct there are no regular ones. There are 4,124 parallelisms with automorphisms of order 5 without fixed points, but none of them is point-transitive.