English

The $\mathrm{L}_3(4)$ near octagon

Combinatorics 2016-10-19 v1

Abstract

In recent work we constructed two new near octagons, one related to the finite simple group G2(4)\mathrm{G}_2(4) and another one as a sub-near-octagon of the former. In the present paper, we give a direct construction of this sub-near-octagon using a split extension of the group L3(4)\mathrm{L}_3(4). We derive several geometric properties of this L3(4)\mathrm{L}_3(4) near octagon, and determine its full automorphism group. We also prove that the L3(4)\mathrm{L}_3(4) near octagon is closely related to the second subconstituent of the distance-regular graph on 486 vertices discovered by Soicher in 1993.

Cite

@article{arxiv.1610.05607,
  title  = {The $\mathrm{L}_3(4)$ near octagon},
  author = {Anurag Bishnoi and Bart De Bruyn},
  journal= {arXiv preprint arXiv:1610.05607},
  year   = {2016}
}

Comments

23 pages

R2 v1 2026-06-22T16:24:13.059Z