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February 2022 Using the 11-point biplane and L2(11) to understand J1
Thomas L. Horine
Rocky Mountain J. Math. 52(1): 105-126 (February 2022). DOI: 10.1216/rmj.2022.52.105

Abstract

In this paper, we use the 11-point biplane and its automorphisms in L2(11) to label and study the Livingstone graph (Γ) and J1, with an aim of using the simplest methods possible. We detail the action of J1 on Γ, along with the adjacencies and coadjacencies (vertices at maximum distance) in Γ. In the last section, we use this apparatus to describe the generation of subgroups of the form 23:7:3 and an elegant substructure of Γ fixed by a maximal subgroup of J1 isomorphic to 19:6.

Citation

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Thomas L. Horine. "Using the 11-point biplane and L2(11) to understand J1." Rocky Mountain J. Math. 52 (1) 105 - 126, February 2022. https://doi.org/10.1216/rmj.2022.52.105

Information

Received: 22 January 2020; Revised: 12 May 2021; Accepted: 13 May 2021; Published: February 2022
First available in Project Euclid: 19 April 2022

Digital Object Identifier: 10.1216/rmj.2022.52.105

Subjects:
Primary: 20D08
Secondary: 05C25

Keywords: Group theory , Janko group , Livingstone graph , Sporadic groups

Rights: Copyright © 2022 Rocky Mountain Mathematics Consortium

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Vol.52 • No. 1 • February 2022
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