Recognition of finite exceptional groups of Lie type

2013/10/10 by Martin W. Liebeck, Liebeck, Martin W., E. A. O’Brien +2
Computer Science · Mathematics · #20C20 #20C40 #Advanced Algebra and Geometry #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #math.GR #msc:20C20 #msc:20C40

paper · pdf · doi:10.48550/arxiv.1310.2978

openalex publication_date 2013/10/10 · arxiv created 2014/09/02 · arxiv updated 2014/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let q be a prime power and let G be an absolutely irreducible subgroup of GL_d(F), where F is a finite field of the same characteristic as \F_q, the field of q elements. Assume that G ≅ G(q), a quasisimple group of exceptional Lie type over \F_q which is neither a Suzuki nor a Ree group. We present a Las Vegas algorithm that constructs an isomorphism from G to the standard copy of G(q). If G \not≅ ³ D₄(q) with q even, then the algorithm runs in polynomial time, subject to the existence of a discrete log oracle.

Citations

• Algorithmic problems in twisted groups of Lie type

Related

• Black box exceptional groups of Lie type
• Computing Green functions in small characteristic
• Embeddings of PSL₂(q) in exceptional groups of Lie type over a field of characteristic ≠2,3
• Exceptional representations of simple algebraic groups in prime characteristic
• Finite type multiple flag varieties of exceptional groups