On a finite group with OS-propermutable Sylow subgroup

IF 0.6 3区 数学 Q3 MATHEMATICS
E. Zubei
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引用次数: 0

Abstract

A Schmidt group is a non-nilpotent group whose every proper subgroup is nilpotent. A subgroup A of a group G is called OS-propermutablein G if there is a subgroup B such that \(G = NG(A)B\), where AB is a subgroup of G and A permutes with all Schmidt subgroups of B. We proved \(p\)-solubility of a group in which a Sylow \(p\)-subgroup is OS-propermutable, where \(p\geq 7\) 7. For \(p < 7\) all non-Abelian composition factors of such group are listed.

具有OS-propermutable Sylow子群的有限群
Schmidt群是一个非幂零群,它的每个固有子群都是幂零的。群G的子群A在G中称为os - propermutableable,如果存在子群B使 \(G = NG(A)B\),其中AB是G的子群,a与b的所有Schmidt子群置换 \(p\)-溶解度的一组,其中的一个黄 \(p\)-subgroup是OS-propermutable,其中 \(p\geq 7\) 7. 因为 \(p < 7\) 列出了该类群的所有非阿贝尔组成因子。
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来源期刊
CiteScore
1.50
自引率
11.10%
发文量
77
审稿时长
4-8 weeks
期刊介绍: Acta Mathematica Hungarica is devoted to publishing research articles of top quality in all areas of pure and applied mathematics as well as in theoretical computer science. The journal is published yearly in three volumes (two issues per volume, in total 6 issues) in both print and electronic formats. Acta Mathematica Hungarica (formerly Acta Mathematica Academiae Scientiarum Hungaricae) was founded in 1950 by the Hungarian Academy of Sciences.
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