Some Multiply Derived Translation Planes with SL(2,5) as an Inherited Collineation Group in the Translation Complement

Arrigo Bonisoli, Gábor Korchmáros, Tamás Szonyi

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

Finite translation planes having a collineation group isomorphic to SL(2, 5) occur in many investigations on minimal normal non-solvable subgroups of linear translation complements. In this paper, we are looking for multiply derived translation planes of the desarguesian plane which have an inherited linear collineation group isomorphic to SL(2, 5). The Hall plane and some of the planes discovered by Prohaska [10], see also [1], are translation planes of this kind of order q2, provided that q is odd and either q2 = 1 mod 5 or q is a power of 5. In this paper the case q2 ≡ -1 mod 5 is considered and some examples are constructed under the further hypothesis that either q ≡ 2 mod 3, or q ≡ 1 mod 3 and q ≡ 1 mod 4, or q ≡ -1 mod 4, 3 (Does not divided) q and q ≡ 3, 5 or 6 mod 7. One might expect that examples exist for each odd prime power q. But this is not always true according to Theorem 2.

Original languageEnglish
Pages (from-to)109-114
Number of pages6
JournalDesigns, Codes, and Cryptography
Volume10
Issue number2
DOIs
Publication statusPublished - Jan 1 1997

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Keywords

  • Multiple derivation
  • Translation plane

ASJC Scopus subject areas

  • Computer Science Applications
  • Applied Mathematics

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