On the principal bundles over a flag manifold.
We study the probability that two elements which are selected at random with replacement from a finite semigroup have the same right matrix.
We review the notion of simple compact quantum groups and examples, and discuss the problem of construction and classification of simple compact quantum groups.
Let be a finite group. The prime graph of is a simple graph whose vertex set is and two distinct vertices and are joined by an edge if and only if has an element of order . A group is called -recognizable by prime graph if there exist exactly nonisomorphic groups satisfying the condition . A 1-recognizable group is usually called a recognizable group. In this problem, it was proved that is recognizable, if is an odd prime and is odd. But for even , only the recognizability...