FINITENESS OF PROFINITE GROUPS WITH A RATIONAL PROBABILISTIC ZETA FUNCTION

被引：0

作者：

Duong Hoang Dung ^{[1
]}

机构：

[1] Univ Bielefeld, Fak Math, Postfach 100131, D-33501 Bielefeld, Germany

来源：

COMMUNICATIONS IN ALGEBRA | 2016年 / 44卷 / 02期

关键词：

Maximal subgroups; Probabilistic zeta function; Profinite groups; SUBGROUPS; CROWNS; INDEX;

D O I：

10.1080/00927872.2014.990023

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that every profinite group in a certain class with a rational probabilistic zeta function has only finitely many maximal subgroups.

引用

页码：787 / 795

页数：9

共 22 条

[1]

Boston N, 1996, PROG MATH, V138, P155

[2] On subgroups with non-zero Mobius numbers in the alternating and symmetric groups [J].

Colombo, Valentina ;

Lucchini, Andrea .

JOURNAL OF ALGEBRA, 2010, 324 (09) :2464-2474

[3]

Detomi E, 2006, LECT NOTES PURE APPL, V243, P47

[4] Crowns and factorization of the probabilistic zeta function of a finite group [J].

Detomi, E ;

Lucchini, A .

JOURNAL OF ALGEBRA, 2003, 265 (02) :651-668

[5] Non-prosoluble profinite groups with a rational probabilistic zeta function [J].

Detomi, Eloisa ;

Lucchini, Andrea .

JOURNAL OF GROUP THEORY, 2007, 10 (04) :453-466

[6] Profinite groups with a rational probabilistic zeta function [J].

Detomi, Eloisa ;

Lucchini, Andrea .

JOURNAL OF GROUP THEORY, 2006, 9 (02) :203-217

[7]

Dung DH, 2013, INT J GROUP THEORY, V2, P167

[8] Rationality of the probabilistic zeta functions of finitely generated profinite groups [J].

Duong Hoang Dung ;

Lucchini, Andrea .

JOURNAL OF GROUP THEORY, 2014, 17 (02) :317-335

[9]

Gaschutz W., 1959, ILLINOIS J MATH, V3, P469

[10] SUBGROUPS OF PRIME POWER INDEX IN A SIMPLE-GROUP [J].

GURALNICK, RM .

JOURNAL OF ALGEBRA, 1983, 81 (02) :304-311

← 1 2 3 →