Philadelphia Area Number Theory Seminar
Wednesday, October 31, 2018 - 2:15pm
Benjamin Pollak
University of Pennsylvania
The inverse Galois problem asks whether every finite group appears as the Galois group of some extension of the rational numbers. In this talk I will focus on which finite groups appear as the Galois group of some extension of the rational numbers in which only a fixed set of primes may ramify. I will present results and examples in some specific cases, with an emphasis on the situation in which only one finite prime ramifies, as well as provide some insight into how the ramified primes in a Galois extension relate to generating sets of the corresponding Galois group.