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Transfer ideals and torsion in the Morava $$E$$-theory of abelian groups. (English) Zbl 07217904
Summary: Let $$A$$ be a finite abelian $$p$$-group of rank at least 2. We show that $$E^0(BA)/I_{tr}$$, the quotient of the Morava $$E$$-cohomology of $$A$$ by the ideal generated by the image of the transfers along all proper subgroups, contains $$p$$-torsion. The proof makes use of transchromatic character theory.
##### MSC:
 55N22 Bordism and cobordism theories and formal group laws in algebraic topology 55P42 Stable homotopy theory, spectra 55S25 $$K$$-theory operations and generalized cohomology operations in algebraic topology
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