Finite Groups with ℙ-Subnormal Sylow Subgroups

被引：0
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作者：
V. N. Kniahina
V. S. Monakhov
机构：
[1] F. Skorina Gomel State University,
来源：
Ukrainian Mathematical Journal | 2021年 / 72卷
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摘要：
Let ℙ be the set of all prime numbers. A subgroup H of a finite group G is called ℙ-subnormal if either H = G or there exists a chain of subgroups H = H0 ≤ H1 ≤ … ≤ Hn = G such that |Hi :  Hi − 1| ∈ ℙ, 1 ≤ i ≤ n. We prove that any finite group with ℙ-subnormal Sylow p-subgroup of odd order is p-solvable and any group with ℙ-subnormal generalized Schmidt subgroups is metanilpotent.
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页码：1571 / 1578
页数：7
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