Tohoku Mathematical Journal
2025
March
SECOND SERIES VOL. 77, NO. 1

Tohoku Math. J.
77 (2025), 17-32

Title HOMOMORPHISMS OF GLOBAL SOLVABLY CLOSED GALOIS GROUPS COMPATIBLE WITH CYCLOTOMIC CHARACTERS

Author Yuichiro Hoshi

(Received December 22, 2021, revised September 22, 2022)
Abstract. In the present paper, we study a continuous open homomorphism between the Galois groups of solvably closed Galois extensions of number fields. We prove that a continuous open homomorphism between the Galois groups of solvably closed Galois extensions of number fields arises from a homomorphism between the given solvably closed Galois extensions if and only if the continuous open homomorphism is compatible with the cyclotomic characters.

Mathematics Subject Classification. Primary 11R32.
Key words and phrases. Galois group, number field, solvably closed, cyclotomic character.

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