David A. Craven

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math.GR2026

The Gill-Guillot commuting graph for sporadic and related groups

David A. Craven, Coen del Valle, Chris Parker

Let $G$ be a finite group and $C$ a normal subset of $G$ . The Gill-Guillot graph has vertices $C$ and $x, y \in C$ are adjacent if and only if $x$ and $…

math.GR2025

On the Maximal Subgroups of $E_{7} (q)$ and Related Almost Simple Groups

David A. Craven

This paper almost classifies the maximal subgroups of $E_{7} (q)$ for general $q$ a power of a prime $p$ . Only four potential maximal subgroups are missing: $P S L_{2} (7)$ (unknown for $p…

math.GR2025

The Ingleton inequality holds for metacyclic groups and fails for supersoluble groups

David A. Craven

The Ingleton inequality first appeared in matroid theory, where Ingleton proved in 1971 that every rank function coming from a representable matroid on four subsets satisfies a par…

The Gill-Guillot commuting graph for sporadic and related groups

On the Maximal Subgroups of E7​(q) and Related Almost Simple Groups

The Ingleton inequality holds for metacyclic groups and fails for supersoluble groups

On the Maximal Subgroups of $E_{7} (q)$ and Related Almost Simple Groups