Dear Forum, Dear Krishna Mohan, > I am using matrices as generators. The set of generators consist of just > 2 elements. Each element by itself generates a small group.
If you have ``random'' matrices the lartge groups you want to exclude likely are very large (containing SL). As a quick way of eliminating such giants, you could (even before trying an orbit calculation) try the orders of a few (pseudo-)random elements (you could replace 20 by a different number): List([1..20],x->Order(PseudoRandom(G))); and calculate the LCM. This is a lower bound for the group order which will typically eliminate very large subgroups of GL very quickly. Also (assuming you're working over a finite field, you could look at the action on submodules or factor modules first: (again they give lower bounds on the order): m:=GModuleByMats(GeneratorsOfGroup(G),DefaultFieldOfMatrixGroup(G)); MTX.IsIrreducible(m); if this returns false, you can use: bas:=MTX.ProperSubmoduleBasis(m); l:=MTX.InducedAction(m,bas); Now l[1].generators gives matrices (in smaller dimension) for the action on the submodule, l[2].generators for the action on the factor module. The orders of the corresponding groups again are lower bounds for |G|. Best, Alexander Hulpke -- Colorado State University, Department of Mathematics, Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA email: hul...@math.colostate.edu, Phone: ++1-970-4914288 http://www.math.colostate.edu/~hulpke _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
