Dear Forum, Dear Watson Ladd, > I am interested in a problem about the lifting of mod > p-representations to p-adic representations. To do this I want to > construct the group Sp(4, Z/2^nZ) for some small > values of n in GAP along with the reduction homomorphisms.
For example: gap> g:=SP(4,Integers mod 32); Sp(4,Z/32Z) gap> gens:=GeneratorsOfGroup(g);; gap> geni:=List(gens,m->List(m,r->List(r,Int)));; # generators as Z matrices gap> geni:=List(gens,m->List(m,r->List(r,Int)))*Z(2); # move to GF(2) gap> h:=Group(geni); <matrix group with 6 generators> gap> hom:=GroupHomomorphismByImagesNC(g,h,gens,geni); (note that the last command will take a bit.) > If I knew generators this would be easy, but I don't. Does anyone have > ideas for what to do? Also, if there are any books I should look at > for the theory that would be useful: I don't know much about this area > yet as I got thrust into it by research demands. May I plug my paper ``Computing generators of groups preserving a bilinear form over residue class rings’’, J.Symb.Comp, 50 (2013), 298-307. DOI 10.1016/j.jsc.2012.08.002 Concerning the structure of these groups, you also might find theorem 2.5 in the joint paper https://arxiv.org/abs/1611.05921 (to appear in Math.Comp.) useful. Best wishes, Alexander Hulpke -- Colorado State University, Department of Mathematics, Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA email: hul...@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
