The behavior of $π$-submaximal subgroups under homomorphisms with $π$-separable kernels

英文摘要：

We explore the extent to which constructing the inductive theory of $\mathfrak{X}$-submaximal subgroups is possible. To this end, we study the behavior of $π$-submaximal subgroups under homomorphisms with $π$-separable kernels and construct examples where such behavior is irregular.