Rank stability of elliptic curves in certain non‐abelian extensions

Abstract Let be an elliptic curve with rank . Fix an odd prime , a positive integer , and a finite abelian extension with rank . In this paper, we show that there exist infinitely many extensions such that is Galois with , and rank . This is an extension of earlier results on rank stability of elliptic curves in cyclic extensions of prime power order to a non‐abelian setting. We also obtain an asymptotic lower bound for the number of such extensions, ordered by their absolute discriminant.