  It is known that locally compact groups approximable by finite ones are
unimodular, but this condition is not sufficient, for example, the simple Lie
groups are not approximable by finite ones as topological groups. In this paper
the approximations of locally compact groups by more general finite algebraic
systems are investigated. It is proved that the approximation of locally
compact groups by finite semigroups is equivalent to approximation by finite
groups and thus not all locally compact groups are approximable by finite
semigroups. We prove that any locally compact group is approximable by finite
left (right) quasigroups but the approximabilty of a locally compact group by
finite quasigroups (latin squares) implies its unimodularity. The question if
the unimodularity of a locally compact group implies its approximability by
finite quasigroups is open. We prove only that the discrete groups are
approximable by finite quasigroups.
