Maximal subgroups of ²E₆(2) and its automorphism groups

2018/01/25 by Robert A. Wilson, Wilson, Robert A.
Mathematics · #20D06 #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.1801.08374

openalex publication_date 2018/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a new computer-assisted proof of the classification of maximal subgroups of the simple group ²E₆(2) and its extensions by any subgroup of the outer automorphism group S₃. This is not a new result, but no earlier proof exists in the literature. A large part of the proof consists of a computational analysis of subgroups generated by an element of order 2 and an element of order 3. This method can be effectively automated, and via statistical analysis also provides a sanity check on results that may have been obtained by delicate theoretical arguments.

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