Abstract
Given a number field \(k\) and an isoclinism class of stem groups (in the sense of P. Hall) it essentially suffices to realize one of these groups as a Galois group over \(k\). Indeed the other groups then appear as Galois groups of subfields of the composita with certain abelian extensions of \(k\) whose existence can be decided by class field theory.
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Schmid, P. Isoclinic Galois groups. Beitr Algebra Geom 56, 763–767 (2015). https://doi.org/10.1007/s13366-014-0234-2
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DOI: https://doi.org/10.1007/s13366-014-0234-2