A local study of group classes

It was established in [15] that the class of groups with a finite commutator subgroup can be locally described by locally graded groups having a bound on the length of particular chains of non-normal subgroups. This approximation was later extended to groups having a finite normal subgroup whose factor group has no non-permutable subgroups (see [18]). The aim of this paper is to show that these approximating group classes behave better than the classes they approximate, and can be used to derive new results on these.

文献[15]已证实，具有有限换位子群（commutator subgroup）的群类，可通过对特定非正规子群（non-normal subgroups）链的长度设置界值的局部分次群（locally graded groups）实现局部刻画。该近似刻画随后被推广至满足如下条件的群：该群存在有限正规子群，且其对应的商群（factor group）不含非置换子群（non-permutable subgroups）（详见文献[18]）。本文旨在证明，上述近似群类比其所近似的原群类具备更优良的性质，且可用于推导对应原群类的全新研究结论。