Fuchs' problem 34 for mixed Abelian groups |
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| Authors: | Ulrich Albrecht |
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| Affiliation: | Department of Mathematics, Auburn University, Auburn, Alabama 36849 |
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| Abstract: | This paper investigates the extent to which an Abelian group  is determined by the homomorphism groups  . A class  of Abelian groups is a Fuchs 34 class if  and  in  are isomorphic if and only if  for all  . Two  -groups  and  satisfy  for all groups  if and only if they have the same  -Ulm-Kaplansky-invariants and the same final rank. The mixed groups considered in this context are the adjusted cotorsion groups and the class  introduced by Glaz and Wickless. While  is a Fuchs 34 class, the class of (adjusted) cotorsion groups is not. |
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| Keywords: | Homomorphism group $p$-group mixed group |
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