Hi, https://math.uni-paderborn.de/fileadmin/mathematik/AG-Computeralgebra/Publications-klueners/gal15.pdf
It's been about 20 years since the publication of this paper by Kluners and Malle and in it they provide a method of determining certain transitive groups of up to degree 15 using the rigidity method for simple groups (as one can see in the tables provided at the end). Furthermore, they additionally provide explicit constructions of polynomials over Q with regards to the transitive subgroups. They mention on page 14 that this was achieved by GAP. My question is twofold: 1) Since it has been 20 years and methods may have changed, is anyone aware of the quickest implementation (an avaiable script) of the rigidity method (section 2.1.1) as mentioned in GAP in order to realize transitive groups up to degree 15 (or higher if it is possible). 2)Additionally, they state a list of varying algorithms in order to determine the polynomials of the associated Galois groups. Is there a standard implementation/script available on GAP for this in having some transitive group of a similar degree (as they've done) and obtain some polynomial to be realized over Q. Many thanks, Mark _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
