具有Engel类条件的可序群
Orderable groups with Engel-like conditions
摘要：
设x是群G中的元素。对于正整数n，设E_n（x）是由所有分解子[. [[y，x]，x]，...，x]在G中的y上，其中x重复n次。最近的一些结果表明，具有小子群E_n（x）的群的某些性质与Engel群的性质接近。本文研究了一类可序群，其中对某些n，子群E_n（x）是循环的.设h，n是正整数，G是一个可序群，其中E_n（x）是多环的，且对G中的每一个x，其Hirsch长度不超过h.证明了存在（h，n）-有界数h* 和c* 使得G有一个n-生成正规幂零子群N，且h（N）<h*，类G/N幂零至多c*.
英文摘要：
Let x be an element of a group G. For a positive integer n let E_n(x) be the subgroup generated by all commutators [...[[y,x],x],...,x] over y in G, where x is repeated n times. There are several recent results showing that certain properties of groups with small subgroups E_n(x) are close to those of Engel groups. The present article deals with orderable groups in which, for some n, the subgroups E_n(x) are polycyclic. Let h,n be positive integers and G an orderable group in which E_n(x) is polycyclic with Hirsch length at most h for every x in G. It is proved that there are (h,n)-bounded numbers h* and c* such that G has a finitely generated normal nilpotent subgroup N with h(N)<h* and G/N nilpotent of class at most c*.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
