Geodesic
Determinability of a completely decomposable rank 3 group by its automorphism group
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 76 (2022), pp. 32-42

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In the work of Vildanov, Gaidak, and Timoshenko, all completely decomposable groups of rank 2 were found that are defined by their automorphism group in the class of all completely decomposable groups. In this article, a similar problem is solved for groups of rank 3. It is shown that a completely decomposable group of rank 3 is determined by its automorphism group if and only if it is a direct sum of three almost divisible summands of rank 1, two of which are isomorphic to each other and embed into the third.
Mots-clés : matrix, automorphism group.
Keywords: involution, completely decomposable group 
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     author = {E. A. Timoshenko and I. V. Tretyakov},
     title = {Determinability of a completely decomposable rank 3 group by its automorphism group},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {32--42},
     publisher = {mathdoc},
     number = {76},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2022_76_a2/}
}
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E. A. Timoshenko; I. V. Tretyakov. Determinability of a completely decomposable rank 3 group by its automorphism group. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 76 (2022), pp. 32-42. http://geodesic.mathdoc.fr/item/VTGU_2022_76_a2/