Sequences of Endomorphism Groups of Abelian Groups |
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Authors: | Timoshenko E A Tsarev A V |
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Institution: | 1.National Research Tomsk State University, Tomsk, 634050, Russia ;2.Moscow State Pedagogical University, Moscow, 119882, Russia ; |
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Abstract: | In the paper, Problem 18.3 of the book “Abelian groups” (2015) by L. Fuchs is solved in the case of Abelian groups with finite p-ranks. For an Abelian group A, a sequence of groups (An) is considered, where A0 = A and An+1 = End An. It is shown that, if all p-ranks of the group A are finite, then this sequence can stabilize either after A0 or after A1. |
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