The notions of periodically defined and residual periodically defined linear transformations of an infinitedimensional vector space V over the field K are introduced. A group of all strictly residual periodically defined transformations and its subgroups of u-periodically defined transformations (where u is a supernatural number) are investigated. A continual family of simple groups obtained as infinite-dimensional analogs of PSL n (K) is constructed.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 10, pp. 1299–1308, October, 2015.
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Bezushchak, O.O., Sushchans’kyi, V.I. Groups of Periodically Defined Linear Transformations of an Infinite-Dimensional Vector Space. Ukr Math J 67, 1457–1468 (2016). https://doi.org/10.1007/s11253-016-1165-x
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DOI: https://doi.org/10.1007/s11253-016-1165-x