相对初等平延群的正规性
Normality of Relative Elementary Tranvection Groups
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中文总结 AI 辅助
本文证明了相对平延群在对应自同构群中是正规的，该结果是对Bak等人关于平延群正规性结论的强化，也是Suslin等人相关正规性结果在模框架下的推广。
中文摘要 AI 辅助
A. A. Suslin与V. I. Kopeiko证明了初等线性群、辛群、正交群分别在一般线性群、辛群、正交群中是正规的，还证明了这些正规性结果对环的理想的相对版本。A. Bak、R. Basu与R. A. Rao证明了线性平延群、辛平延群、正交平延群分别在各自的自同构群中是正规的，这些结果是Suslin和Kopeiko在模的框架下正规性结果的推广。本文中，我们证明了Bak、Basu和Rao所证正规性结果的更强版本，即相对平延群在各自的自同构群中是正规的。
英文摘要
A. A. Suslin and V. I. Kopeiko proved that the elementary linear, symplectic, and orthogonal groups are normal in the general linear group, symplectic group, and orthogonal group respectively. They also proved relative versions of these normality results with respect to an ideal of a ring. A. Bak, R. Basu, and R. A. Rao proved that the linear, symplectic, and orthogonal transvection groups are normal in the respective automorphism groups. These results are generalizations of the normality results by Suslin and Kopeiko in the setup of modules. In this paper, we prove stronger versions of the normality results proved by Bak, Basu, and Rao, which say that the relative transvection groups are normal in the respective automorphism groups.
