2- группы, обладающие автоморфизмом нечетного порядка, тождественным на инволюциях.
We prove that the type factor generated by the regular representation of is isomorphic to its tensor product with the hyperfinite type factor. This implies that the unitary group of is contractible with respect to the topology defined by the natural Hilbertian norm.
Let be a finite group and construct a graph by taking as the vertex set of and by drawing an edge between two vertices and if is cyclic. Let be the set consisting of the universal vertices of along the identity element. For a solvable group , we present a necessary and sufficient condition for to be nontrivial. We also develop a connection between and when is divisible by two distinct primes and the diameter of is 2.