Dear Forum, I have read in wikipedia that there are following 3-transposition groups. See below quote from wikipedia article on "3-transposition groups". I have no problem to obtain in GAP groups SO(1,n,2), Omega(1,n,2), PSU(n,2), Sp(n,2). I can also define Fischer groups Fi22, Fi23, Fi24 using Atlas package. I have only trouble with O+-(2n,3) case. E.g. neither SO(1,6,3) nor Omega (1,6,3) is 3-transposition group. What is the way to define the 3-transposition group defined under case Oμ, π(*n*, 3) below.
Regards, Marek ---------------------------------- Suppose that *G* is a group that is generated by conjugacy class of 3-transpositions and such that the 2 and 3 cores<http://en.wikipedia.org/wiki/P-core> *O*2(*G*) and *O*3(*G*) are both contained in the center *Z*(*G*) of *G*and the derived group of *G* is perfect. Then Fischer (1971<http://en.wikipedia.org/wiki/3-transposition_group#CITEREFFischer1971>) proved that up to isomorphism *G*/*Z*(*G*) is one of the following groups and *D* is the image of the given conjugacy class: - *G*/*Z*(*G*) is a symmetric group *Sn*, and *D* is the class of transpositions. - *G*/*Z*(*G*) is a symplectic group Sp(2*n*, 2) over the field of order 2, and *D* is the class of transvections - *G*/*Z*(*G*) is a projective special unitary group PSU(*n*, 2), and *D*is the class of transvections - *G*/*Z*(*G*) is an orthogonal group Oμ(2*n*, 2), and *D* is the class of transvections - *G*/*Z*(*G*) is an index 2 subgroup Oμ, π(*n*, 3) of the orthogonal group Oμ(*n*, 3) generated by the class *D* of reflections of norm π vectors, where μ and π can be 1 or -1. - *G*/*Z*(*G*) is one of the three Fischer groups<http://en.wikipedia.org/wiki/Fischer_group>Fi 22, Fi23, Fi24. If the condition that the derived group of *G* is perfect is dropped there are two extra cases: - *G*/*Z*(*G*) is one of two groups containing on orthogonal group O+(8, 2) or O-(8, 3) with index 3. _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
