G-covering subgroup systems for the classes of supersoluble and nilpotent groups

被引：67

作者：

Guo, WB ^{[1
]}

Shum, KP

Skiba, A

机构：

[1] Xuzhou Normal Univ, Dept Math, Xuzhou 221009, Peoples R China

[2] Univ Sci & Technol China, Dept Math, Hefei 230026, Peoples R China

[3] Chinese Univ Hong Kong, Fac Sci, Shatin, Hong Kong, Peoples R China

[4] Fr Skaryna Gomel State Univ, Dept Math, Gomel 246019, BELARUS

来源：

ISRAEL JOURNAL OF MATHEMATICS | 2003年 / 138卷 / 1期

关键词：

Normal Subgroup; Maximal Subgroup; Nilpotent Group; Sylow Subgroup; Minimal Normal Subgroup;

D O I：

10.1007/BF02783422

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let F be a class of groups and G a group. We call a set Sigma of subgroups of G a G-covering subgroup system for the class F (or directly a F-covering subgroup system of G) if G is an element of F whenever every subgroup in Sigma is in F. In this paper, we provide some nontrivial sets of subgroups of a finite group G which are simultaneously G-covering subgroup systems for the classes of supersoluble and nilpotent groups.

引用

页码：125 / 138

页数：14

共 10 条

[1]

[Anonymous], IZV AKAD NAUK SSSR M

[2] ON FINITE-GROUPS WITH NILPOTENT SYLOW-NORMALIZERS [J].

BIANCHI, M ;

MAURI, AGB ;

HAUCK, P .

ARCHIV DER MATHEMATIK, 1986, 47 (03) :193-197

[3]

CUNIHIN SA, 1930, CR HEBD ACAD SCI, V191, P397

[4] MINIMAL NICHT UBERAUFLOSBARE ENDLICHE GRUPPEN [J].

DOERK, K .

MATHEMATISCHE ZEITSCHRIFT, 1966, 91 (03) :198-&

[5]

Doerk K., 1992, GRUYTER EXP MATH, V4

[6] FINITE SOLUBLE GROUPS WITH SUPERSOLUBLE SYLOW NORMALIZERS [J].

FEDRI, V ;

SERENA, L .

ARCHIV DER MATHEMATIK, 1988, 50 (01) :11-18

[7]

Gorenstein D., 1980, FINITE GROUPS

[8]

Huppert B., 1967, Endliche Gruppen I, VI

[9]

Huppert B., 1954, Math. Z, V60, P409, DOI DOI 10.1007/BF01187387

[10]

Kargapolov MI, 1979, FUNDAMENTALS THEORY

← 1 →