Geodesic
An $\mathfrak X$-crown of a finite soluble group
Algebra i logika, Tome 49 (2010) no. 5, pp. 591-614

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Let $G$ be a finite soluble group and $\Phi_\mathfrak X(G)$ an intersection of all those maximal subgroups $M$ of $G$ for which $G/\mathrm{Core}_G(M)\in\mathfrak X$. We look at properties of a section $F(G/\Phi_\mathfrak X(G))$, which is definable for any class $\mathfrak X$ of primitive groups and is called an $\mathfrak X$-crown of a group $G$. Of particular importance is the case where all groups in $\mathfrak X$ have equal socle length.
Keywords: finite soluble group, crown, prefrattini subgroup. 
@article{AL_2010_49_5_a1,
     author = {S. F. Kamornikov and L. A. Shemetkov},
     title = {An $\mathfrak X$-crown of a~finite soluble group},
     journal = {Algebra i logika},
     pages = {591--614},
     publisher = {mathdoc},
     volume = {49},
     number = {5},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2010_49_5_a1/}
}
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S. F. Kamornikov; L. A. Shemetkov. An $\mathfrak X$-crown of a finite soluble group. Algebra i logika, Tome 49 (2010) no. 5, pp. 591-614. http://geodesic.mathdoc.fr/item/AL_2010_49_5_a1/