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JOURNALS // Problemy Fiziki, Matematiki i Tekhniki (Problems of Physics, Mathematics and Technics) // Archive

PFMT, 2010 Issue 1(2), Pages 16–21 (Mi pfmt149)

MATHEMATICS

On irreduñible soluble local formations which íàóå $p$-decomposable defect 3

V. V. Aniskov

F. Skorina Gomel State University, Gomel

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.

UDC: 512.542

Received: 04.03.2010



© Steklov Math. Inst. of RAS, 2024