Geodesic
Generalized Frattini Subgroups as Coradicals of Groups
Matematičeskie zametki, Tome 87 (2010) no. 3, pp. 402-411

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The paper deals with finite solvable groups only. It is established that the class of all regular subgroup $m$-functors coincides with the class of all $X$-abnormal $m$-functors, where $X$ ranges over all subclasses of the class of all primitive groups. The properties of the lattice of all regular subgroup $m$-functors are studied and the atoms and coatoms of this lattice are described. It is proved that the generalized Frattini subgroup of $G$ corresponding to a regular $m$-functor coincides with the $X$-coradical of $G$ for some $R_0$-closed class $X$.
Mots-clés : finite solvable group
Keywords: Frattini subgroup, regular subgroup $m$-functor, Boolean lattice, primitive group, formation of groups, primitivator. 
@article{MZM_2010_87_3_a7,
     author = {S. F. Kamornikov},
     title = {Generalized {Frattini} {Subgroups} as {Coradicals} of {Groups}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {402--411},
     publisher = {mathdoc},
     volume = {87},
     number = {3},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2010_87_3_a7/}
}
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S. F. Kamornikov. Generalized Frattini Subgroups as Coradicals of Groups. Matematičeskie zametki, Tome 87 (2010) no. 3, pp. 402-411. http://geodesic.mathdoc.fr/item/MZM_2010_87_3_a7/