FINITE GROUPS WITH SUBNORMAL RESIDUALS OF SYLOW NORMALIZERS

被引：1
|
作者：
Vasil'eva, T., I [1 ]
Koranchuk, A. G. [2 ]
机构：
[1] Belarusian State Univ Transport, Gomel, BELARUS
[2] Francisk Skorina Gomel State Univ, Gomel, BELARUS
来源：
SIBERIAN MATHEMATICAL JOURNAL | 2022年 / 63卷 / 04期
关键词：
finite group; Sylow normalizer; subnormal subgroup; formation; X-residual; supersolvable group; SATURATED FORMATIONS; SOLUBLE GROUPS; SUBGROUPS;
D O I：
10.1134/S0037446622040073
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Considering a nonempty formation X of nilpotent groups, we prove that a group G is an extension of a nilpotent group by an X-group if and only if every Sylow normalizer in G is solvable and its X-residual is subnormal in G. We also show that G is supersolvable if and only if every Sylow normalizer in G is supersolvable and its nilpotent residual is subnormal in G.
引用
收藏
页码：670 / 676
页数：7
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