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Problemy Fiziki, Matematiki i Tekhniki (Problems of Physics, Mathematics and Technics), 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
References:
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.
Received: 04.03.2010
Document Type: Article
UDC: 512.542
Language: Russian
Citation: V. V. Aniskov, “On irreduñible soluble local formations which íàóå $p$-decomposable defect 3”, PFMT, 2010, no. 1(2), 16–21
Citation in format AMSBIB
\Bibitem{Ani10}
\by V.~V.~Aniskov
\paper On irreduñible soluble local formations which íàóå $p$-decomposable defect 3
\jour PFMT
\yr 2010
\issue 1(2)
\pages 16--21
\mathnet{http://mi.mathnet.ru/pfmt149}
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