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.
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页数：20
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