A criterion of elementary equivalence of automorphism groups of reduced Abelian p-groups
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Consider reduced Abelian p-groups (p ≥ 3) A 1 and A 2. In this paper, we prove that the automorphism groups Aut A 1 and Aut A 2 are elementary equivalent if and only if the groups A 1 and A 2 are equivalent in second-order logic bounded by the cardinalities of the basic subgroups of A 1 and A 2.
KeywordsAutomorphism Group Endomorphism Ring Associative Ring Chevalley Group Basic Subgroup
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