The discussion revolves around the relationship between finite groups and Galois groups of polynomials in the rational numbers, specifically questioning whether every finite group can be realized as the Galois group of some polynomial in Q.
Some participants have identified the question as related to the Inverse Galois Problem, noting that the complete answer to this problem is not fully known. There is an acknowledgment of the complexity of the topic, with some expressing interest in further exploration.
Participants reflect on their previous learning experiences in Galois theory, indicating a potential gap in understanding this specific aspect of the theory. There is a suggestion that the question may seem obvious to some, highlighting varying levels of familiarity with the topic.
That's not a question. Given that a finite group G is isomorphic to the Galois group of some polynomial, what? What conclusion are you to make?futurebird said:Given a finite group G is G isomorphic to the Galois group of some polynomial in Q? Having done a course on Galois theory I think I just missed this and I feel like I ought to know the answer. Did I just sleep through that part of class?
:/
Dunkle said:I think what the question is asking is the following. If you are given some finite group, is it isomorphic to the Galois group of some polynomial in Q?