Affiliation:
1. All-Russian Academy of International Trade
Abstract
We give necessary and sufficient conditions for the embedding
of a quadratic extension of a number field $k$ into an extension
with group of generalized quaternions; in this case, the case
of both a cyclic kernel and a generalized quaternion is considered.
As a consequence, it is proved that the class of ultrasolvable
$2$-extensions with cyclic kernel does not coincide with the class
of non-semidirect extensions. Sufficient conditions are also given
for the embedding of quadratic extensions $k(\sqrt{d_1})/k$,
$k(\sqrt{d_2})/k$, $k(\sqrt{d_1d_2})/k$ of a number field $k$
into a generalized quaternion extension $L/k$. Related examples are given.
Publisher
Steklov Mathematical Institute