English

The structure of $3$-pyramidal groups

Group Theory 2023-02-28 v2 Combinatorics

Abstract

A combinatorial block design DD is called 33-pyramidal if there exists a subgroup GG of \mboxAut(D)\mbox{Aut}(D) fixing 33 points and acting regularly on the other points. If this happens, we say that the design is 33-pyramidal under GG. In case DD is a Kirkman triple system, it is known that such a group GG has precisely 33 involutions, all conjugate to each other. In this paper, we obtain a classification of the groups with this property.

Keywords

Cite

@article{arxiv.2302.12285,
  title  = {The structure of $3$-pyramidal groups},
  author = {Xiaofang Gao and Martino Garonzi},
  journal= {arXiv preprint arXiv:2302.12285},
  year   = {2023}
}
R2 v1 2026-06-28T08:48:18.484Z