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

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