Abstract
We study D-hyperoctahedral groups, diagonal inductive limits of hyperoctahedral groups. Also, we describe the Z 2-modules of periodic sequences over diagonal limits of symmetric groups under their action on the elements of a Z 2-module by permutation of coordinates. The imprimitivity systems for D-hyperoctahedral groups are characterized, and a full description of the lattices of their normal subgroups is given.
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Original Russian Text Copyright © 2014 Oliynyk B.V. and Sushchanskiĭ V.I.
The first author was financially supported by the State Agency for Science, Innovations, and Informatization of Ukraine (Grant 0112U005849).
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 55, No. 1, pp. 165–177, January–February, 2014.
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Oliynyk, B.V., Sushchanskiĭ, V.I. Imprimitivity systems and lattices of normal subgroups in D-hyperoctahedral groups. Sib Math J 55, 132–141 (2014). https://doi.org/10.1134/S0037446614010169
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DOI: https://doi.org/10.1134/S0037446614010169