Abstract

This article was inspired by the inverse problem of Galois theory. Galois groups are realized as number theoretic symmetry groups realized physically in TGD a symmetries of space-time surfaces. Galois confinement is as analog of color confinement is proposed in TGD inspired quantum biology. Two instances of the inverse Galois problem, which are especially interesting in TGD, are following: Q1: Can a given finite group appear as Galois group over Q? The answer is not known. Q2: Can a given finite group G appear as a Galois group over some EQ? Answer to Q2 is positive as will be found and the extensions for a given G can be explicitly constructed.