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Twisted burnside theory for the discrete Heisenberg group and for wreath products of some groups

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Abstract

For each positive integer N, an automorphism with the Reidemeister number 2N of the discrete Heisenberg group is constructed; an example of determination of points in the unitary dual object being fixed with respect to the mapping induced by the group automorphism is given. For wreath products of finitely generated Abelian groups and the group of integers, it is proved that if the Reidemeister number of an arbitrary automorphism is finite, then it is equal to the number of fixed points of the induced mapping on a finite-dimensional part of the unitary dual object.

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory, Moscow, 119991, Russia

    F. K. Indukaev

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  1. F. K. Indukaev
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Original Russian Text © F.K. Indukaev, 2007, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2007, Vol. 62, No. 6, pp. 9–17.

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Indukaev, F.K. Twisted burnside theory for the discrete Heisenberg group and for wreath products of some groups. Moscow Univ. Math. Bull. 62, 219–227 (2007). https://doi.org/10.3103/S0027132207060022

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