Abstract
Let G be a finite group. A subgroup H of G is \({\mathbb {P}}\) -subnormal in G whenever either \(H=G\) or there exists a chain of subgroups \({H=H_0\le H_1\le \cdots \le H_n=G}\), such that \(|H_{i}:H_{i-1}|\) is a prime for every \(i=1, \ldots , n\); G is said to be \(\mathrm {w}\) -supersoluble if every Sylow subgroup of G is \({\mathbb {P}}\)-subnormal in G. We study conditions under which the group \(G=AB\), where A and B are \(\mathbb P\)-subnormal subgroups of G, belongs to a subgroup-closed saturated formation containing all finite supersoluble groups and contained in the class of all \(\mathrm {w}\)-supersoluble groups.
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Monakhov, V.S., Trofimuk, A.A. On Products of Finite \(\mathrm {w}\)-Supersoluble Groups. Mediterr. J. Math. 18, 100 (2021). https://doi.org/10.1007/s00009-021-01744-2
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DOI: https://doi.org/10.1007/s00009-021-01744-2
Keywords
- Factorized groups
- \({\mathrm {w}}\)-supersoluble groups
- \({{\mathbb {P}}}\)-subnormal subgroup
- sylow subgroups
- \(\mathfrak {X}\)-residual