-groups.
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.
For a finite group , , the intersection graph of , is a simple graph whose vertices are all nontrivial proper subgroups of and two distinct vertices and are adjacent when . In this paper, we classify all finite nonsimple groups whose intersection graphs have a leaf and also we discuss the characterizability of them using their intersection graphs.