PreprintCC BY 4.0arXiv
Automorphisms of pentagonal geometries with block size 3
Abstract
A pentagonal geometry PENT(k,r) is a k-uniform, r-regular partial linear space with the property that the set of points not collinear with a given point x is itself a line in the geometry. The existence spectrum of these geometries is known; we begin the study of automorphisms of these structures in the case k=3. We determine the spectrum of pentagonal geometries PENT(3,r) with either a cyclic or reverse automorphism to be r = 1 or 10 (mod 12). In addition, we show that there are 584 pairwise non-isomorphic PENT(3,7)s and classify them by the orders of their automorphism groups.
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BibTeX
@misc{erskine2026automorphisms,
title = {{Automorphisms of pentagonal geometries with block size 3}},
author = {Grahame Erskine and Terry S. Griggs},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01390},
eprint = {2610.01390},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01390},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Automorphisms of pentagonal geometries with block size 3
AU - Grahame Erskine
AU - Terry S. Griggs
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01390
UR - https://arxiv.org/abs/2610.01390
AB - A pentagonal geometry PENT(k,r) is a k-uniform, r-regular partial linear space with the property that the set of points not collinear with a given point x is itself a line in the geometry. The existence spectrum of these geometries is known; we begin the study of automorphisms of these structures in the case k=3. We determine the spectrum of pentagonal geometries PENT(3,r) with either a cyclic or reverse automorphism to be r = 1 or 10 (mod 12). In addition, we show that there are 584 pairwise non-isomorphic PENT(3,7)s and classify them by the orders of their automorphism groups.
ER -