Recently M. Mathieu [9] has proved that any associative ultraprime normed complex algebra is centrally closed. The aim of this note is to announce the general nonassociative extension of Mathieu's result obtained by the authors [2].
We discuss some examples of nonassociative algebras which occur in VOA (vertex operator algebra) theory and finite group theory. Methods of VOA theory and finite group theory provide a lot of nonassociative algebras to study. Ideas from nonassociative algebra theory could be useful to group theorists and VOA theorists.