On Baer's Theorem and Its Generalizations

被引：1

作者：

Taghavi, Yasaman ^{[1
]}

Kayvanfar, Saeed ^{[1
]}

Parvizi, Mohsen ^{[1
]}

机构：

[1] Ferdowsi Univ Mashhad, Dept Pure Math, POB 1159, Mashhad 91775, Razavi Khorasan, Iran

来源：

MEDITERRANEAN JOURNAL OF MATHEMATICS | 2021年 / 18卷 / 06期

关键词：

Schur's theorem; Baer's theorem; hypercenter; nilpotent group; SCHUR;

D O I：

10.1007/s00009-021-01887-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A well known theorem of R. Baer states that if G is a group and G/Z(n)(G) is finite, then gamma(n+1)(G) is finite. In this article, we extend this theorem for groups G that have subgroups A of Aut(G) such that A/Inn(G) is finitely generated or is of finite special rank. Furthermore, some new upper bounds for vertical bar gamma(n+1)(G)vertical bar and vertical bar gamma(n+1)(G, A)vertical bar are presented.

引用

页数：20

共 50 条

[31] Some generalizations of Bohr's theorem
Hamada, Hidetaka
Honda, Tatsuhiro
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2012, 35 (17) : 2031 - 2035
[32] New Generalizations of Fueter's Theorem
Kou, Kit-Ian
NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS, VOLS A-C, 2011, 1389
[33] Ideal generalizations of Egoroff's theorem
Repicky, Miroslav
ARCHIVE FOR MATHEMATICAL LOGIC, 2020, 59 (7-8) : 957 - 977
[34] SOME GENERALIZATIONS OF OLIVIER'S THEOREM
Faisant, Alain
Grekos, Georges
Misik, Ladislav
MATHEMATICA BOHEMICA, 2016, 141 (04): : 483 - 494
[35] Combinatorial Generalizations of Jung’s Theorem
Arseniy V. Akopyan
Discrete & Computational Geometry, 2013, 49 : 478 - 484
[36] Uniform generalizations of Fueter’s theorem
Baohua Dong
Tao Qian
Annali di Matematica Pura ed Applicata (1923 -), 2021, 200 : 229 - 251
[37] Generalizations of Cantor's theorem in ZF
Shen, Guozhen
MATHEMATICAL LOGIC QUARTERLY, 2017, 63 (05) : 428 - 436
[38] Some generalizations of Montel's theorem
Cartwright, ML
PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1935, 31 : 26 - 30
[39] On Halphen's theorem and some generalizations
Lins Neto, Alcides
ANNALES DE L INSTITUT FOURIER, 2006, 56 (06) : 1947 - 1982
[40] Uniform generalizations of Fueter's theorem
Dong, Baohua
Qian, Tao
ANNALI DI MATEMATICA PURA ED APPLICATA, 2021, 200 (01) : 229 - 251

← 1 2 3 4 5 →