| dc.description.abstract |
We propound a descent principle by which previously constructed equations
over GF.qn/.X/ may be deformed to have incarnations over GF.q/.X/ without
changing their Galois groups. Currently this is achieved by starting with a vectorial
(= additive) q-polynomial of q-degreemwith Galois group GL.m; q/ and then, under
suitable conditions, enlarging its Galois group to GL.m; qn/ by forming its generalized
iterate relative to an auxiliary irreducible polynomial of degree n. Elsewhere
this was proved under certain conditions by using the classification of finite simple
groups, and under some other conditions by using Kantor’s classification of linear
groups containing a Singer cycle. Now under different conditions we prove it by
using Cameron-Kantor’s classification of two-transitive linear groups. |
en_US |