Mathematical Sciences Seminar - Presentations for orthogonal groups?
When:
—
Venue:
Birkbeck Main Building, Malet Street
No booking required
< a1 , ... , am | ai3 = 1, for all i, (ai aj )2 = 1, i ≠ j >
is a well-known presentation for the alternating group Am+2 . In 1982, Sidki asked the question: what if we allow the generators ai to have order n rather than just order 3? He conjectured that the group y(m, n) given by this presentation was finite. Some results in small cases are known and the conjecture appears to hold (with an interesting pattern of groups occurring), but the question is still open. This problem has links to classical groups defined over rings and Clifford algebras. We will discuss our work on the conjecture and how we plan to solve it. This is joint work with Sergey Shpectorov and Said Sidki.
Contact name:
Department of Economics, Mathematics and Statistics