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| Content Provider | Springer Nature Link |
|---|---|
| Author | Ezquerro, L. M. Soler Escrivà, X. |
| Copyright Year | 2007 |
| Abstract | In this paper, we prove the following result. Let $${\mathfrak{F}}$$ be a saturated formation and Σ a Hall system of a soluble group G. Let X be a w-solid set of maximal subgroups of G such that Σ reduces into each element of X. Consider in G the following three subgroups: the $${\mathfrak{F}}$$ -normalizer D of G associated with Σ; the X-prefrattini subgroup W = W(G,X) of G; and a hypercentrally embedded subgroup T of G. Then the lattice $${\mathfrak{L}(T,W,D)}$$ generated by T,D and W is a distributive lattice of pairwise permutable subgroups of G with the cover and avoidance property.This result remains true for the lattice $${\mathfrak{L}(V,W,D)}$$ , where V is a subgroup of G whose Sylow subgroups are also Sylow subgroups of hypercentrally embedded subgroups of G such that Σ reduces into V. |
| Ending Page | 2078 |
| Page Count | 10 |
| Starting Page | 2069 |
| File Format | |
| ISSN | 14398516 |
| e-ISSN | 14397617 |
| Journal | Acta Mathematica Sinica, English Series |
| Issue Number | 11 |
| Volume Number | 23 |
| Language | English |
| Publisher | Springer-Verlag |
| Publisher Date | 2007-02-15 |
| Publisher Place | Berlin/Heidelberg |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | Series and lattices of subgroups lattice properties Products of subgroups Chains and lattices of subgroups, subnormal subgroups factorizations cover and avoidance properties Mathematics Subnormal subgroups permutability Sylow subgroups, Sylow properties, $\pi$-groups, $\pi$-structure |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics |
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