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arXiv · 2610.24325

The prime graph complements of $\mathcal{A}_{11}$- and $\mathcal{A}_{13}$-solvable groups

Logan Abounader·Austin Bell·April Beun·Elvis Cabrera·Dakota Nobuyuki Goto·Thomas Michael Keller
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Abstract

We study prime graph complements of $\mathcal{A}_n$-solvable groups, focusing on the cases $\mathcal{A}_{11}$ and $\mathcal{A}_{13}$. These provide the first classifications of $T$-solvable groups for which $|π(T)|>4$. We develop structural and representation-theoretic tools for analyzing the possible prime graph complements and use them to obtain complete characterizations for both $\mathcal{A}_{11}$-solvable and $\mathcal{A}_{13}$-solvable groups. The methods introduced also provide a framework for studying analogous classification problems for larger alternating groups.

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Logan Abounader, Austin Bell, April Beun, Elvis Cabrera, Dakota Nobuyuki Goto, Thomas Michael Keller. 2026-10-16. The prime graph complements of $\mathcal{A}_{11}$- and $\mathcal{A}_{13}$-solvable groups. https://arxiv.org/abs/2610.24325

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