On irreduсible soluble local formations which науе $p$-decomposable defect 3

V. V. Aniskov

Problemy fiziki, matematiki i tehniki, no. 1 (2010), pp. 16-21

Résumé

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.

Détail

Keywords: finite group, class of groups, lattice, lenglh of lattice, irreducible local formation
Mots-clés : local formation, local chain, $p$-decomposable group, soluble local formalion.