Recognising the small Ree groups in their natural representations
Group Theory
2014-08-29 v3 Data Structures and Algorithms
Abstract
We present Las Vegas algorithms for constructive recognition and constructive membership testing of the Ree groups 2G_2(q) = Ree(q), where q = 3^{2m + 1} for some m > 0, in their natural representations of degree 7. The input is a generating set X. The constructive recognition algorithm is polynomial time given a discrete logarithm oracle. The constructive membership testing consists of a pre-processing step, that only needs to be executed once for a given X, and a main step. The latter is polynomial time, and the former is polynomial time given a discrete logarithm oracle. Implementations of the algorithms are available for the computer algebra system MAGMA.
Cite
@article{arxiv.1206.0411,
title = {Recognising the small Ree groups in their natural representations},
author = {Henrik Bäärnhielm},
journal= {arXiv preprint arXiv:1206.0411},
year = {2014}
}