Elementary equivalence of endomorphism rings and automorphism groups of periodic Abelian groups
| Autor: | Bunina, Elena |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this paper, we prove that the endomorphism rings End A and End A' of periodic infinite Abelian groups A and A' are elementarily equivalent if and only if the endomorphism rings of their p-components are elementarily equivalent for all primes p. Additionally, we show that the automorphism groups Aut A and Aut A' of periodic Abelian groups A and A' that do not have 2-components and do not contain cocyclic p-components are elementarily equivalent if and only if, for any prime p, the corresponding p-components A_p and A_p' of A and A' are equivalent in second-order logic if they are not reduced, and are equivalent in second-order logic bounded by the cardinalities of their basic subgroups if they are reduced. For such groups A and A', their automorphism groups are elementarily equivalent if and only if their endomorphism rings are elementarily equivalent, and the automorphism groups of the corresponding p-components for all primes p are elementarily equivalent. Comment: 12 pages |
| Databáze: | arXiv |
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