Bibliographic Details
| Title: |
The structure of $3$-pyramidal groups |
| Authors: |
Gao, Xiaofang, Garonzi, Martino |
| Publication Year: |
2023 |
| Collection: |
Mathematics |
| Subject Terms: |
Mathematics - Group Theory, Mathematics - Combinatorics |
| More Details: |
A combinatorial block design $D$ is called $3$-pyramidal if there exists a subgroup $G$ of $\mbox{Aut}(D)$ 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. |
| Document Type: |
Working Paper |
| Access URL: |
http://arxiv.org/abs/2302.12285 |
| Accession Number: |
edsarx.2302.12285 |
| Database: |
arXiv |
