Multiplicative groups of fields and hereditarily irreducible polynomials
  In this paper we explore the concept of {\em good heredity} for fields from a group theoretic perspective. Extending results from \cite{alice}, we show that several natural families of fields are of good heredity, and some others are not. We also construct several examples to show that various wishful thinking expectations are not true. 
Alice Medvedev and Ramin Takloo-Bighash
math.RA math.NT