Recognition of finite exceptional groups of Lie type

Martin W. Liebeck; E. A. O'Brien

Recognition of finite exceptional groups of Lie type

Group Theory 2014-09-03 v2

Authors: Martin W. Liebeck , E. A. O'Brien

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 $G \cong G(q)$ , 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.

Keywords

finite exceptional groups lie type recognition algorithm las vegas algorithm isomorphism construction discrete log oracle polynomial time

Cite

@article{arxiv.1310.2978,
  title  = {Recognition of finite exceptional groups of Lie type},
  author = {Martin W. Liebeck and E. A. O'Brien},
  journal= {arXiv preprint arXiv:1310.2978},
  year   = {2014}
}

Recognition of finite exceptional groups of Lie type

Abstract

Keywords

Cite

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