The structure of 3-pyramidal groups

2023/02/23 by Xiaofang Gao, Martino Garonzi, Gao, Xiaofang +1
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2302.12285

openalex publication_date 2023/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A combinatorial block design D is called 3-pyramidal if there exists a subgroup G of Aut(D) fixing 3 points and acting regularly on the other points. If this happens, we say that the design is 3-pyramidal under G. In case D is a Kirkman triple system, it is known that such a group G has precisely 3 involutions, all conjugate to each other. In this paper, we obtain a classification of the groups with this property.

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