On the power-commutative kernel of locally nilpotent groups.
In this paper as the main result, we determine finite groups with the same prime graph as the automorphism group of a sporadic simple group, except .
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.