可容许性和领域关系
Admissibility and field relations
摘要：
设K是一个数域。一个有限群G称为K-容许群，如果存在一个G-交叉积K-除代数. K-可容许性有一个必要条件，称为K-预容许性，已知在许多情况下是充分的。判定Q上两个不同次数的数域K和L是否有相同的容许群是一个20年前的公开问题。我们构造了无穷多对数域（K，L），使得K是L的一个真子域，且K和L具有相同的预容许群.这为否定回答这个问题提供了证据。特别是，它遵循的建设，K和L有相同的奇数阶容许群。
英文摘要：
Let K be a number field. A finite group G is called K-admissible if there exists a G-crossed product K-division algebra. K-admissibility has a necessary condition called K-preadmissibility that is known to be sufficient in many cases. It is a 20 year old open problem to determine whether two number fields K and L with different degrees over Q can have the same admissible groups. We construct infinitely many pairs of number fields (K,L) such that K is a proper subfield of L and K and L have the same preadmissible groups. This provides evidence for a negative answer to the problem. In particular, it follows from the construction that K and L have the same odd order admissible groups.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
