Recognition of finite exceptional groups of Lie type
Copyright policy )Recognition of finite exceptional groups of Lie type
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 $G \cong G(q)$, 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 $G \not\cong {}^3 D_4(q)$ with $q$ even, then the algorithm runs in polynomial time, subject to the existence of a discrete log oracle.
- University of Auckland New Zealand
- Imperial College United Kingdom
- Imperial College London United Kingdom
General Mathematics, Group Theory (math.GR), 20C20, 20C40, Symbolic computation and algebraic computation, exceptional groups of Lie type, Linear algebraic groups over finite fields, ELEMENTS, constructive recognition, FOS: Mathematics, SUBGROUPS, Simple groups: alternating groups and groups of Lie type, Science & Technology, FAST CONSTRUCTIVE RECOGNITION, NATURAL REPRESENTATIONS, Pure Mathematics, CLASSICAL-GROUPS, Las Vegas algorithms, Physical Sciences, Exceptional groups, Software, source code, etc. for problems pertaining to group theory, finite quasisimple groups, Mathematics - Group Theory, Mathematics, Computational methods (representations of groups)
General Mathematics, Group Theory (math.GR), 20C20, 20C40, Symbolic computation and algebraic computation, exceptional groups of Lie type, Linear algebraic groups over finite fields, ELEMENTS, constructive recognition, FOS: Mathematics, SUBGROUPS, Simple groups: alternating groups and groups of Lie type, Science & Technology, FAST CONSTRUCTIVE RECOGNITION, NATURAL REPRESENTATIONS, Pure Mathematics, CLASSICAL-GROUPS, Las Vegas algorithms, Physical Sciences, Exceptional groups, Software, source code, etc. for problems pertaining to group theory, finite quasisimple groups, Mathematics - Group Theory, Mathematics, Computational methods (representations of groups)
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