Abstract:
All groups considered are finite. Let $\mathfrak{H}$ be a class of groups, $\mathfrak{F}$ be a local formation. We denote by $\mathfrak{F}/_l\mathfrak{F} \cap \mathfrak{H}$ the lattice of local formations concluded between $\mathfrak{F}$ and $\mathfrak{F} \cap \mathfrak{H}$ has finite length $n$ , then $n$ is called the $\mathfrak{H}$-defect $\mathfrak{F}$. A local formation $\mathfrak{F}$ is called reducible if $\mathfrak{F} = $lform$(\bigcup\limits_{i \in I} \mathfrak{F}_i )$, where $\{\mathfrak{F}_i \mid i \in I\}$ is the set of all nontrivial local subformation of $\mathfrak{F}$. In this paper we obtain the exact description of irreducible soluble local formations with $p$-decomposable defect 3.
Keywords:finite group, class of groups, local formation, lattice, lenglh of lattice, local chain, $p$-decomposable group, irreducible local formation, soluble local formalion.