Compositional formations of $c$-length~3

V. A. Vedernikov ; D. G. Koptyukh

Diskretnaya Matematika, Tome 13 (2001) no. 1, pp. 119-131

Résumé

Let $\Theta$ be a full modular lattice of the formation of finite groups and let $0_\Theta$ be zero of $\Theta$. We say that a $\Theta$-formation $\mathfrak F\ne 0_\Theta$ has the $\Theta$-length $l_\Theta(\mathfrak F)$ equal to $n$ if there exist $\Theta$-formations $$ \mathfrak F_0,\mathfrak F_1, \ldots,\mathfrak F_n $$ such that $\mathfrak F_n=\mathfrak F$, $\mathfrak F_0=0_\Theta$, and $\mathfrak F_{i-1}$ is a maximal $\Theta$-subformation of $\mathfrak F_i$, $i=1,\ldots,n$. In this paper, a complete description of the structure of composite formations of the $c$-length 3 is obtained.