(2,3,7)-generated groups of small rank
Chiara Tamburini, Università Cattolica del Sacro Cuore
Friday May 19, 2.30-3.15, Groups in Galway 2006
A group G is said to be (2,3,7)-generated (or Hurwitz, if finite) if
it can be generated by two elements x,y, of respective orders 2 and 3,
such that xy has order 7. In this talk, after a brief survey of the
finite simple groups that are known to be Hurwitz, I will concentrate
on the irreducible (2,3,7)-generated subgroups of PGLn(F),
where F is an algebraically closed field of characteristic p (possibly
0) and n is small. It is possible to give a full classification for
n<=5. The same methods lead to the discovery of new Hurwitz groups for
n=6,7.