Orthogonal and oriented Fano planes, triangular embeddings of $ K_7, $ and geometrical representations of the Frobenius group $ F_{21} $

Orthogonal and oriented Fano planes, triangular embeddings of $ K_7, $ and geometrical representations of the Frobenius group $ F_{21} $

In this paper we present some geometrical representations of $ F_{21}, $ the Frobenius group of order $ 21 $. The main focus is on investigating the group of common automorphisms of two orthogonal Fano planes and the automorphism group of a suitably oriented Fano plane. We show that both groups are...

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Bibliographic Details
Main Authors: Simone Costa, Marco Pavone
Format: Article
Language:English
Published: AIMS Press 2024-12-01
Series:AIMS Mathematics
Subjects:
orthogonal fano planes
oriented fano plane
frobenius group $ f_{21} $
toroidal embedding
kirkman triple system
sts($ 15 $), kts($ 15 $)
Online Access:https://www.aimspress.com/article/doi/10.3934/math.20241676
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https://www.aimspress.com/article/doi/10.3934/math.20241676

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