自同构不变性与恒等式
Automorphism invariance and identities
摘要：
如果一个外（多线性）交换子恒等式在群的一个大子群中成立，那么它也在一个大的特征子群中成立。类似的断言对于代数及其理想或子空间也是有效的。改变“大”这个词的含义，我们得到许多有趣的事实。这些结果不能推广到任意（非多线性）身份。作为一个应用，我们给出了一个尖锐的估计的“虚拟导出长度”（虚拟可解）的（虚拟可解）的群体。
英文摘要：
If an outer (multilinear) commutator identity holds in a large subgroup of a group, then it holds also in a large characteristic subgroup. Similar assertions are valid for algebras and their ideals or subspaces. Varying the meaning of the word "large", we obtain many interesting facts. These results cannot be extended to arbitrary (non-multilinear) identities. As an application, we give a sharp estimate for the `virtual derived length' of (virtually solvable)-by-(virtually solvable) groups.
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。
