Geodesic
Finite groups with formational subnormal primary subgroups of bounded exponent
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 785-796.

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Let $\mathfrak{U}_k$ be the class of all supersoluble groups in which exponents are not divided by the $(k+1)$-th powers of primes. We investigate the classes $\mathrm{w}\mathfrak{U}_k$ and $\mathrm{v}\mathfrak{U}_k$ that contain all finite groups in which every Sylow and, respectively, every cyclic primary subgroup is $\mathfrak{U}_k$-subnormal. We prove that $\mathrm{w}\mathfrak{U}_k$ and $\mathrm{v}\mathfrak{U}_k$ are subgroup-closed saturated formations and obtain the characterizations of these formations.
Keywords: finite group, primary subgroup, subnormal subgroup. 
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V. S. Monakhov; I. L. Sokhor. Finite groups with formational subnormal primary subgroups of bounded exponent. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 785-796. http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a4/

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