Dear Lenny, "maximal parabolic" presentations for all classical groups were given by Chevalley and Tits (my attribution is from memory, so can be a bit off)
In the case of L(n,2), such a presentation is in terms of generators of the form Eij, i<>j, where is Eij a matrix with 1 at the entry (i,j) and on the main diagonal, 0 elsewhere. More precisely, you only need to take Eij with i<j and j=i+i. (The subgroups generated by all Eij except one Epq, q=p-1, are called maximal parabolics) Write down presentations for each L(3,2) that sits in a 3x3-submatrix on the main diagonal; take the resulting relations, the relations that Eij commutes with Epq (for all pairs ij, pq where this happens), the relations defining the upper triangular subgroup B=<Eij|i<j>, and the relations arising from describing the action of each Eij, j=i-1 on B (i.e. of the form Eij Epq Eij=X(i,p,q), X(i,p,q) an element of B). Finally, add relations Eij^2=1. The result is a (faithful) presentation for L(n,2). Hope this helps, Dmitrii On Sat, Nov 14, 2009 at 03:33:12AM +0800, lenny wrote: > Dear Forum: > > The Atlas has presentations for L(5,2) and L(7,2), > but none for L(4,2) or L(6,2). Gap can fing one for L(4,2), > but my computer runs out of memmory when trying to find onw for L(6,2). > Is one known? > > Lenny Chastkofsky > > _______________________________________________ > Forum mailing list > Forum@mail.gap-system.org > http://mail.gap-system.org/mailman/listinfo/forum CONFIDENTIALITY: This email is intended solely for the person(s) named. The contents may be confidential and/or privileged. If you are not the intended recipient, please delete it, notify us, and do not copy or use it, nor disclose its contents. Thank you. Towards A Sustainable Earth: Print Only When Necessary _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
