Let \( \mathbb{X} \) be a subset of the set of positive integers. A subgroup H of a group G is called \( \mathbb{X} \)-subnormal in G if there exists a chain of subgroups H = H 0 ⊆ H 1 ⊆ … ⊆ H n = G such that |H i : H i-1| ∈ \( \mathbb{X} \) for all i . We study the solubility and r -solubility of a finite group G = AB with some restrictions imposed on the subgroups A and B and on the set \( \mathbb{X} \) .
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, No. 10, pp. 1431–1435, October, 2014.
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Tyutyanov, V.N., Knyagina, V.N. Factorizations of Finite Groups into r-Soluble Subgroups with Given Embeddings. Ukr Math J 66, 1603–1608 (2015). https://doi.org/10.1007/s11253-015-1036-x
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DOI: https://doi.org/10.1007/s11253-015-1036-x