The Yang-Baxter Equation and Characteristic Finite Simple Quotients of the Free Group of Rank 2

2025/10/03 by Hanany, Liam · 1 citation
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2510.03210

Abstract

We show that infinitely many alternating groups arise as quotients of the free group of rank 2, with kernel a characteristic subgroup. We also show that such simple quotients exist of arbitrarily large Lie rank. This resolves two questions posed by arXiv:2308.14302

Citations

• Families of elliptic curves over the four-pointed configuration space and exceptional sequences for the braid group on four strands
• Infinite simple characteristic quotients
• Finite simple characteristic quotients of the free group of rank 2
• On TQFT representations of mapping class groups with boundary
• Markoff Surfaces and Strong Approximation: 1
• Dynamics of Aut(Fn) Actions on Group Presentations and Representations
• Nonabelian Algebraic Topology
• Braid Groups are Linear

Cited by

• Characteristic Subgroup Growth

Related

• Finite simple characteristic quotients of the free group of rank 2
• Infinite simple characteristic quotients
• Alternating quotients of free groups
• Abelian fixed point free endomorphisms and the Yang-Baxter equation
• Indecomposable solutions of the Yang-Baxter equation with permutation group of sizes pq and p²q