Baumann-components of finite groups of characteristic p, general theory

In this paper we introduce a new conjugacy class Baup(G) of p-subgroups of finite groups G of characteristic p. We then prove some factorization and decomposition theorems related to this conjugacy class. In particular, these results show that the only obstructions for B∈Baup(G) being normal in G are the Baumann components of G, a class of subnormal subgroups E with E/Op(E) quasisimple or SL2(p)′ for p≤3.