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Problemy Fiziki, Matematiki i Tekhniki (Problems of Physics, Mathematics and Technics), 2010, Issue 1(2), Pages 16–21
(Mi pfmt149)
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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.
Received: 04.03.2010
Citation:
V. V. Aniskov, “On irreduñible soluble local formations which íàóå $p$-decomposable defect 3”, PFMT, 2010, no. 1(2), 16–21
Linking options:
https://www.mathnet.ru/eng/pfmt149 https://www.mathnet.ru/eng/pfmt/y2010/i1/p16
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Abstract page: | 103 | Full-text PDF : | 57 | References: | 28 |
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