Sylow Objects in Finite Groups and the Factorization of Formations
by
Guo Wenbin
Department of Mathematics, Xuzhou Normal University, Xuzhou 221116, P.R.China

It is well known that the classic Sylow theorem is the most important result of groups and has numerous applications. In particular, we should mention that Sylow objects such as p-subgroups and their normalizers have played an important role in the problems of classification of finite simple groups.

Within the framework of the theory of formations, Sylow objects also played an important role. Remenber that if a finite group G belongs to a saturated formation \frakF and G has a composition factor of order p, then the class \frakN_p of all finite p-groups is contained in \frakF. Analogy to Sylow subgroups is seen here, therefore the formations of the \frakN_p type can be called Sylow objects in the theory of formations.

In this report, we give a brief introduction on some of the new research along the two directions.

Date received: February 13, 2006