A construction and characterization of new sharply 3-transitive permutation sets contained in \(P\varGamma L(2,K)\)
type: Item
instance of: scholarly article
title: A construction and characterization of new sharply 3-transitive permutation sets contained in \(P\varGamma L(2,K)\)
zbMATH Open document ID: 1489.51002
author: Carla Fiori
published in: Mediterranean Journal of Mathematics
publication date: 2022-01-03T00:00:00Z
review text: A set \(S\) of permutations on a finite set \(\Omega\) is said to be sharply \(k\)-transitive if for any two \(k\)-tuples \((x_1,\cdots,x_k)\) and \((y_1,\cdots,y_k)\) of distinct elements in \(\Omega\), there exists a unique permutation \(\alpha\in S\) such that \(x_i^{\alpha}=y_i\) for \(i=1,\cdots,k\). Sharply \(k\)-transitive permutation sets have various applications in the construction of combinatorial and geometric structures. The main contribution of this paper is a charaterization of the sharply 3-transitive permutation groups and sets in \(P\Gamma L(2,K)\) whose permutations are defined from two automorphisms of the finite field \(K\). It covers all known sharply 3-transitive permutation groups and sets on \(K\cup \{\infty\}\), and it also provides new constructions.
reviewed by: Yue Zhou
Mathematics Subject Classification ID: 51B20
Mathematics Subject Classification ID: 20B20
Mathematics Subject Classification ID: 51E25
zbMATH DE Number: 7451587
zbMATH Keywords: sharply 3-transitive permutation sets
zbMATH Keywords: invertible permutation sets
zbMATH Keywords: Minkowski plane
MaRDI profile type: Publication
full work available at URL: s00009-021-01923-1
OpenAlex ID: W3217722118
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DOI: 10.1007/S00009-021-01923-1
description: scientific article; zbMATH DE number 7451587