The nilpotent π-length of finite π-solvable groups with restrictions on subgroups

被引：0

作者：

Shpyrko O.A. ^{[1
]}

机构：

[1] Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory

来源：

Moscow University Mathematics Bulletin | 2008年 / 63卷 / 1期

关键词：

Solvable Group; Proper Subgroup; Minimal Normal Subgroup; Hall Subgroup; Fitting Subgroup;

D O I：

10.1007/s11970-008-1005-9

中图分类号：

学科分类号：

摘要：

V.S. Monakhov's conjecture concerning an estimate of the nilpotent π-length of a π-solvable group G is confirmed in the case l p(G) ≤ 1 for all p ∈ π {q} and q ∈ π. New estimates of the nilpotent π-length of a π-solvable group with a supersolvable π-Hall subgroup are also obtained. © 2008 Allerton Press, Inc.

引用

页码：22 / 26

页数：4

共 12 条

[1]

Huppert B., Endliche Gruppen I, (1967)

[2]

Hall P., Higman G., On the p-Length of p-Solvable Groups and Reduction Theorems for Burnside's Problem, Proc. London Math. Soc., 3, (1956)

[3]

Chernikov N.S., Petravchuk A.P., Characterization of Periodical Locally Solvable Groups with Solvable and with Finite-Exponent Sylow π-Subgroups, Ukr. Matem. Zhurn., 39, 6, (1987)

[4]

Kourovskaya Tetrad, (2006)

[5]

Chernikov N.S., Petravchuk A.P., The π Length of Finite π-Solvable Groups, Infinite Groups and Adjacent Algebraic Structures, Trudy Inst. Matem. Ukrainy, pp. 393-405, (1993)

[6]

Kazarin L.S., Solvable Product of Groups, Infinite Groups 94, pp. 111-123, (1995)

[7]

Monakhov V.S., Shpyrko O.A., On the Nilpotent π-Length of a Finite π-Solvable Group, Discret. Matem., 13, 3, (2001)

[8]

Shpyrko O.A., Hall Subgroups and Nilpotent π-Length of a π-Solvable Group, Vestsi NAN Belarusi, Ser. Fiz.-Matem. Navuk, 2, (2001)

[9]

Semenchuk V.N., The Class of Finite Solvable Groups, Doklady Akad. Nauk BSSR, 104, (1976)

[10]

Chernikov S.N., Groups with Given Properties of Subgroup Systems, (1980)

← 1 2 →