Geodesic
Involutions of the automorphism group of a completely decomposable finite-rank Abelian group
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 86 (2023), pp. 167-175 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the framework of the study of questions of the definability of a completely decomposable Abelian group of finite rank by its group of automorphisms, it is shown that any set of pairwise permutable involutions of such a group of automorphisms, which has some additional properties, is conjugate with a set of diagonal involutions.
Keywords: completely decomposable group, involution
Mots-clés : automorphism group, matrix. 
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     title = {Involutions of the automorphism group of a completely decomposable finite-rank {Abelian} group},
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E. A. Timoshenko; I. V. Tretyakov. Involutions of the automorphism group of a completely decomposable finite-rank Abelian group. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 86 (2023), pp. 167-175. http://geodesic.mathdoc.fr/item/VTGU_2023_86_a12/

[1] Vildanov V.K., “Opredelyaemost vpolne razlozhimoi abelevoi gruppy bez krucheniya ranga 2 svoei gruppoi avtomorfizmov”, Vestnik Nizhegorodskogo universiteta im. N.I. Lobachevskogo, 3:1 (2011), 174–177

[2] Vildanov V.K., “Determinability of a completely decomposable block-rigid torsion-free Abelian group by its automorphism group”, j. Math. Sci. (New York), 197:5 (2014), 590594 | DOI | MR

[3] Vildanov V.K., “On determinability of a completely decomposable torsion-free Abelian group by its automorphism group”, j. Math. Sci. (New York), 230:3 (2018), 372–376 | DOI | MR | Zbl

[4] Vildanov V.K., Opredelyaemost abelevoi gruppy ee gruppoi avtomorfizmov i tsentrom koltsa endomorfizmov, dis. ... kand. fiz.-mat. nauk, N. Novgorod, 2014 | Zbl

[5] Timoshenko E.A., Tretyakov I.V., “Opredelyaemost vpolne razlozhimoi gruppy ranga 3 ee gruppoi avtomorfizmov”, Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, 2022, no. 76, 32–42 | DOI | Zbl

[6] Fuks L., Beskonechnye abelevy gruppy, v. 2, Mir, M., 1977

[7] Tretyakov I.V., Timoshenko E.A., “Involyutsii v gruppe avtomorfizmov vpolne razlozhimoi gruppy”, Vse grani matematiki i mekhaniki, vseros. molodezhnaya nauch. konf. studentov, sb. st., Izd-vo NTL, Tomsk, 2021, 139–154

[8] Henriksen M., “Two classes of rings generated by their units”, j. Algebra, 31:1 (1974), 182–193 | DOI | MR | Zbl