Abstract
A finite groupG is calledQ-admissible if there exists a finite dimensional central division algebra overQ, containing a maximal subfield which is a Galois extension ofQ with Galois group isomorphic toG. It is proved thatS5−, one of the two nontrivial central extensions ofS5 byZ/2Z, isQ-admissible. As a consequence of that result and previous results of Sonn and Stern, every finite Sylow-metacyclic group, havingA5 as a composition factor, isQ-admissible.
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