Presentations

Using presentations, find a canonical example of a monoid on a given set of generators that has the property that the intersection of prinicipal right ideals is finitely generated but not principal. Find a presentation corresponding to idempotent generators of the singular ideal of the partial endomorphism monoid of a finitely generated free G-Act F_n(G). This will build on work of James East for PT_n and the full endomorphism monoid of F_n(G). Find presentations of ideals of M_n(D) for a division ring D. Investigate the subgroup structure of pseudo-reductive groups, starting with an investigation of the orders of elements in their (geometric) unipotent radicals.