Holonomy groups of compact flat solvmanifolds are exactly the finite abelian groups, with minimal dimensions for cyclic groups matching those of general compact flat manifolds.
Bieberbach, Über die Bewegungsgruppen der Euklidischen Räume I, Math
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Holonomy groups of compact flat solvmanifolds
Holonomy groups of compact flat solvmanifolds are exactly the finite abelian groups, with minimal dimensions for cyclic groups matching those of general compact flat manifolds.