Recognising the small Ree groups in their natural representations

We present Las Vegas algorithms for constructive recognition and constructive membership testing of the Ree groups (2)G(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 subset of GL(7, q). 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. (C) 2014 Elsevier Inc. All rights reserved.