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Designs, Codes and Cryptography

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03-02-2020

Flag-transitive block designs with prime replication number and almost simple groups

Authors: Seyed Hassan Alavi, Mohsen Bayat, Jalal Choulaki, Ashraf Daneshkhah

Published in: Designs, Codes and Cryptography | Issue 5/2020

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Abstract

In this article, we study 2-designs with prime replication number admitting a flag-transitive automorphism group. The automorphism groups of these designs are point-primitive of almost simple or affine type. We determine 2-designs with prime replication number admitting an almost simple automorphism group and prove that such a design belongs to one of two infinite families of projective spaces or Witt-Bose-Shrikhande spaces or it is isomorphic to a design with parameters (6, 3, 2), (8, 4, 3), (11, 5, 2) or (12, 6, 5).

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Title: Flag-transitive block designs with prime replication number and almost simple groups
Authors: Seyed Hassan Alavi
Mohsen Bayat
Jalal Choulaki
Ashraf Daneshkhah
Publication date: 03-02-2020
Publisher: Springer US
Published in: Designs, Codes and Cryptography / Issue 5/2020
Print ISSN: 0925-1022
Electronic ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-020-00724-z

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Flag-transitive block designs with prime replication number and almost simple groups

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