Unramified extensions of quadratic number fields with Galois group 2. Aₙ

Key Points

• Infinitely many groups 2.An are realized as unramified extensions in quadratic number fields, enhancing number theory.
• This research provides the first comprehensive realizations of infinite covering groups in this context.
• The study builds on previous works that only addressed conditional results, thus marking a significant advancement.
• Use of Galois group theory establishes deeper connections between number fields and their algebraic structures.

Abstract