Groups of Periodically Defined Linear Transformations of an Infinite-Dimensional Vector Space

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 PSLn(K) is constructed.