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In 2009 Ekedahl introduced certain cohomological invariants of finite groupswhich are naturally related to the Noether Problem. We show that theseinvariants are trivial for every finite group in GL_3(k) and for the fifthdiscrete Heisenberg group H_5. Moreover in the case of finite linear groupswith abelian projective reduction, these invariants satisfy a recurrencerelation in a certain Grothendieck group for abelian groups.

The Ekedahl Invariants for finite groups