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Subgroups of odd depth—a necessary condition

Sebastian Burciu (2013)

Czechoslovak Mathematical Journal

This paper gives necessary and sufficient conditions for subgroups with trivial core to be of odd depth. We show that a subgroup with trivial core is an odd depth subgroup if and only if certain induced modules from it are faithful. Algebraically this gives a combinatorial condition that has to be satisfied by the subgroups with trivial core in order to be subgroups of a given odd depth. The condition can be expressed as a certain matrix with { 0 , 1 } -entries to have maximal rank. The entries of the matrix...

Subgroups of the Baer–Specker group with few endomorphisms but large dual

Andreas Blass, Rüdiger Göbel (1996)

Fundamenta Mathematicae

Assuming the continuum hypothesis, we construct a pure subgroup G of the Baer-Specker group 0 with the following properties. Every endomorphism of G differs from a scalar multiplication by an endomorphism of finite rank. Yet G has uncountably many homomorphisms to ℤ.

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