In this paper, we study non-central almost subnormal subgroups of the multiplicative group of a division ring satisfying a nonzero generalized rational identity. The main result generalizes Chiba’s theorem on subnormal subgroups. As an application, we get a theorem on almost subnormal subgroups satisfying a generalized algebraic rational identity. The last theorem has several corollaries which generalize completely or partially some previous results.

中文翻译：

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具有广义代数有理恒等式的除环中的几乎次正规子群

在本文中，我们研究满足非零广义有理恒等式的除环乘法群的非中心几乎次正规子群。主要结果将千叶定理推广到次正规子群。作为一个应用，我们得到了一个关于满足广义代数有理恒等式的几乎次正规子群的定理。最后定理有几个推论，它们完全或部分地推广了一些先前的结果。