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Bassian-Finite Abelian Groups

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We introduce a new class of Abelian groups which lies strictly between the classes of co-Hopfian groups and Dedekind-finite groups, calling these groups {\it Bassian-finite}. We prove the surprising fact that in the torsion case the Bassian-finite property coincides with the co-Hopficity, thus extending a recent result by Chekhlov-Danchev-Keef in Siber.
Danchev, Peter V., Keef, Patrick W.
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On finite abelian 𝑝-groups [PDF]

open access: yesBulletin of the American Mathematical Society, 1939
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