The Golod-Shafarevich theorem is a result bounding the relations required in presentations of certain finitely generated algebras and p-groups. One consequence is that some class field towers are infinite (Golod and Shafarevich 1964). In other words, repeatedly passing from a number field to its Hilbert class field need not terminate.
Golod-Shafarevich Theorem
See also
Class Field Tower, Graded Algebra, Group Presentation, Hilbert Series, p-GroupExplore with Wolfram|Alpha
References
Golod, E. S. and Shafarevich, I. R. "On the Class Field Tower." Izv. Akad. Nauk SSSR Ser. Mat. 28, 261-272, 1964.Cite this as:
Weisstein, Eric W. "Golod-Shafarevich Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Golod-ShafarevichTheorem.html