We describe an algorithm to compute a composition tree for a matrix group defined over a
finite field, and show how to use the associated structure to carry out computations with such …

Let G=〈 X〉⩽ GL (d, F) be a classical group in its natural representation defined over a finite
field F of odd characteristic. We present Las Vegas algorithms to construct standard …

Towards effective algorithms for linear groups Page 171 Towards effective algorithms for linear
groups EA O’Brien Abstract. One of the major research directions in computational group theory …

Algorithms for matrix groups Page 12 ALGORITHMS FOR MATRIX GROUPS EA O'BRIEN
Department of Mathematics, University of Auckland, Auckland, New Zealand Email: obrien …

Given a finite group G and a faithful irreducible FG-module V where F has prime order, does
G have a regular orbit on V? This problem is equivalent to determining which primitive …

Given a finite group G and a faithful irreducible FG-module V where F has prime order, does
G have a regular orbit on V? This problem is equivalent to determining which primitive …

Abstract We present Las Vegas algorithms for constructive recognition and constructive
membership testing of the Ree groups G 2 2 (q)= Ree (q), where q= 3 2 m+ 1 for some m> 0 …

Aschbacher's Theorem [1] subdivides maximal subgroups of the classical groups and their
almost simple extensions into nine classes, denoted C1,…, C9. The first eight of these …

Abstract We generalize the Plesken–Fabiańska L 2-quotient algorithm for finitely presented
groups on two or three generators to allow an arbitrary number of generators. The main …

Under the assumption of a certain conjecture, for which there exists strong experimental
evidence, we produce an efficient algorithm for constructive membership testing in the …