Topic
Classical involution theorem
About: Classical involution theorem is a research topic. Over the lifetime, 2 publications have been published within this topic receiving 21 citations.
Papers
TL;DR: In this paper, the authors give a partial answer to the Cherlin-Zil'ber Conjecture, which states that every infinite simple group of finite Morley rank is isomorphic to an algebraic group over an algebraically closed field.
17 citations
Posted Content•
TL;DR: In this paper, a one-sided Monte-Carlo algorithm was proposed to construct a long root subgroup in a black-box group of odd order, where the structure of the centralizers of the involutions of the group is analyzed.
Abstract: We present a one sided Monte--Carlo algorithm which constructs a long root $\sl_2(q)$-subgroup in $X/O_p(X)$, where $X$ is a black-box group and $X/O_p(X)$ is a finite simple group of Lie type defined over a field of odd order $q=p^k > 3$ for some $k\geqslant 1$. Our algorithm is based on the analysis of the structure of centralizers of involutions and can be viewed as a computational version of Aschbacher's Classical Involution Theorem. We also present an algorithm which determines whether the $p$-core (or "unipotent radical") $O_p(X)$ of a black-box group $X$ is trivial or not, where $X/O_p(X)$ is a finite simple classical group of odd characteristic $p$. This answers a well-known question of Babai and Shalev.
12 citations
Performance Metrics
| Year | Papers |
|---|---|
| 2010 | 1 |
| 2001 | 1 |