In this survey we discuss the approximations of topological groups by finite algebraic systems: groups, semigroups, quasigroups and loops. In this chapter we discuss the approximations of topological groups by finite algebraic systems. The definition of approximation that we explore was introduced in [9] for investigation of the approximation of locally compact a'belian groups by finite abelian groups. According to this definition (Definition 13.1) the approximating finite groups are embedded into the locally compact group G that they approximate only as sets and their group laws converge to the group law of G in the topology of the uniform convergence on compacts. This definition arose from the consideration of representation of numbers in the computer, see Examples 13.2 and 13.3 in 13.3.1.
展开▼
