Clifford theory for group-graded rings.
There are investigated some closure conditions of Thomsen type in 3-webs which gurantee that at least one of coordinatizing quasigroups of a given 3-web is commutative.
I consider p-Bernoulli bond percolation on transitive, nonamenable, planar graphs with one end and on their duals. It is known from [BS01] that in such a graph G we have three essential phases of percolation, i.e. , where is the critical probability and -the unification probability. I prove that in the middle phase a.s. all the ends of all the infinite clusters have one-point boundaries in ∂ℍ². This result is similar to some results in [Lal].