Abstract
We study twisted conjugacy classes of the unit element in different groups. Fel’shtyn and Troitsky showed that the twisted conjugacy class of the unit element of an abelian group is a subgroup for every automorphism. The structure is investigated of a group whose twisted conjugacy class of the unit element is a subgroup for every automorphism (inner automorphism).
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Original Russian Text Copyright © 2013 Bardakov V.G., Nasybullov T.R., and Neshchadim M.V.
The authors were supported by the Program “Development of the Scientific Potential of Higher School” (Grant 2.1.1.10726), the Interdisciplinary Project of the Siberian Division of the Russian Academy of Sciences (Grant 44-2012), and the Federal Target Program “Scientific and Scientific-Pedagogical Personnel of Innovative Russia” for 2009–2013 (State Contract 02.740.11.5191).
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Translated from Sibirskiı Matematicheskiı Zhurnal, Vol. 54, No. 1, pp. 20–34, January–February, 2013.
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Bardakov, V.G., Nasybullov, T.R. & Neshchadim, M.V. Twisted conjugacy classes of the unit element. Sib Math J 54, 10–21 (2013). https://doi.org/10.1134/S0037446613010023
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DOI: https://doi.org/10.1134/S0037446613010023