Finite groups with small centralizers of word-values

被引：1

作者：

Detomi, Eloisa ^{[1
]}

Morigi, Marta ^{[2
]}

Shumyatsky, Pavel ^{[3
]}

机构：

[1] Univ Padua, Dipartimento Matemat Tullio Levi Civita, Via Trieste 63, I-35121 Padua, Italy

[2] Univ Bologna, Dipartimento Matemat, Piazza Porta San Donato 5, I-40126 Bologna, Italy

[3] Univ Brasilia, Dept Math, BR-70910900 Brasilia, DF, Brazil

来源：

MONATSHEFTE FUR MATHEMATIK | 2020年 / 191卷 / 02期

关键词：

Group words; Centralizers; Commutators;

D O I：

10.1007/s00605-019-01292-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given a positive integer m and a group-word w, we consider a finite group G such that w(G)not equal 1 and all centralizers of non-trivial w-values have order at most m. We prove that if w=v(x1q1,MIDLINE HORIZONTAL ELLIPSIS,xkqk), where v is a multilinear commutator word and q1,MIDLINE HORIZONTAL ELLIPSIS,qk are p-powers for some prime p, then the order of G is bounded in terms of w and m only. Similar results hold when w is the nth Engel word or the word w=[xn,y1,MIDLINE HORIZONTAL ELLIPSIS,yk] with k >= 1.

引用

页码：257 / 265

页数：9

共 10 条

[1]

Chernikov N. S., 1993, INFINITE GROUPS RELA, P393

[2] On right n-Engel subgroups [J].