Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Institutions: Texas State University, Massachusetts Institute of Technology
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222993858