Geodesic
On Hereditary Superradical Formations of Full Characteristic
Matematičeskie zametki, Tome 112 (2022) no. 1, pp. 76-82

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A formation $\mathfrak{F}$ of finite groups is said to be superradical if it satisfies the following requirements: $\bullet$ $\mathfrak{F}$ is a normally hereditary formation; $\bullet$ any group $G=AB$, where $A$ and $B$ are $\mathfrak{F}$-subnormal $\mathfrak{F}$-subgroups in $G$, belongs to $\mathfrak{F}$. The paper presents an infinite series of hereditary superradical formations of full characteristic that are not solvably saturated. This completes the negative answer to question 14.99 (b) in “Kourovka Notebook”.
Keywords: finite group, generalized subnormal subgroup, superradical formation, solvably saturated formation.
Mots-clés : formation 
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X. Yi; X. Wan; S. F. Kamornikov. On Hereditary Superradical Formations of Full Characteristic. Matematičeskie zametki, Tome 112 (2022) no. 1, pp. 76-82. http://geodesic.mathdoc.fr/item/MZM_2022_112_1_a6/