The Universal Nonabelian Representation of the Petersen Type Geometry Related toJ4 Original Research Article

Let image be a geometry with three points on each line. The universal representation groupR(image) of image is generated by a set of involutions, one for each point, subject to the relations that for every line the product of the three generators corresponding to the points on the line is the identity. LetJ4be the fourth sporadic simple group of Janko and let image(J4) be the Petersen type geometry ofJ4whose points and lines are subgroups of order 2 and 22inJ4with normalizers containing Sylow 2-subgroups; the incidence relation is given by inclusion. We show thatR(image(J4)) is exactlyJ4.