Gudzenko S. . Factorpowers of symmetryc group of of denumerable order.

The work deals with the countable order symmetric group factorpower. Different representations of the arbitrary group factorpower elements are presented ant teir properties are investigated. The descriptions of the idempotents and maximal subgroups of the countable order symmetric group factorpower are obtained. The initary subsemigroups of the countable order symmetric group factorpower are introduced, their relations are obtained, Grren's relations for the countable order symmetric group factorpower and it's finitary subsemigroups are described. The construction of the automorphisms of the countable order symmetric group factorpower and it's finitary subsemigroups are described.