Autor:	C, Aruna, Vanchinathan, P
Rok vydání:	2023
Předmět:	Mathematics - Number Theory 11R04 12F05
Druh dokumentu:	Working Paper
Popis:	For each real quadratic field we constructively show the existence of infinitely many exceptional quartic number fields containing that quadratic field. On the other hand, another infinite collection of quartic exceptional fields without any quadratic subfields is also provided. Both these families are non-Galois extensions of $\mathbf{Q}$, and their normal closu res have Galois groups $D_4$ and $S_4$ respectively. We also show that an infinite number of these exceptional quartic fields have power integral basis, i.e., monogenic. We also construct large collections of exceptional number fields in all degrees greater than 4. Comment: 13 pages. Conjecture in earlier version is proved
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2306.17556 Zobrazit plný text záznamu View this record from Arxiv