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

[1] On Baer’s Theorem and Its Generalizations
Yasaman Taghavi
Saeed Kayvanfar
Mohsen Parvizi
Mediterranean Journal of Mathematics, 2021, 18
[2] ON SOME GENERALIZATIONS OF BAER'S THEOREM
Kurdachenko, L. A.
Pypka, O. O.
CARPATHIAN MATHEMATICAL PUBLICATIONS, 2014, 6 (02) : 310 - 316
[3] On Copson's Theorem and Its Generalizations
Linero Bas, A.
Nieves Roldan, D.
DIFFERENTIAL AND DIFFERENCE EQUATIONS WITH APPLICATIONS, 2018, 230 : 339 - 349
[4] Szasz's theorem and its generalizations
Bourdaud, Gerard
ARCHIV DER MATHEMATIK, 2022, 118 (01) : 79 - 90
[5] On Craig's theorem and its generalizations
Provost, SB
JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 1996, 53 (03) : 311 - 321
[6] Szasz’s theorem and its generalizations
Gérard Bourdaud
Archiv der Mathematik, 2022, 118 : 79 - 90
[7] A generalization of Baer's theorem
Zhang, Xinjian
COMMUNICATIONS IN ALGEBRA, 2017, 45 (11) : 4971 - 4973
[8] A VARIANT OF BAER'S THEOREM
Zusmanovich, Pasha
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2024, 54 (03) : 929 - 932
[9] A converse of Baer's theorem
Hatamian R.
Hassanzadeh M.
Kayvanfar S.
Ricerche di Matematica, 2014, 63 (1) : 183 - 187
[10] The epimorphism theorem and its generalizations
Dutta, Amartya K.
Gupta, Neena
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2015, 14 (09)

← 1 2 3 4 5 →