Lanne’s T-functor and Hypersurfaces
Lanne’s T-functor and Hypersurfaces
投稿时间:2016-09-17  最后修改时间:2017-08-20
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中文关键词:  
英文关键词:T-functor, Hypersurface, Pointwise stabilizers
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作者单位E-mail
Zheng Wenhua 大连理工大学数学科学学院 673952966@qq.com 
Nan Jizhu 大连理工大学数学科学学院 jznan@163.com 
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英文摘要:
      Through discussing the transformation of the invariant ideals, we ?rstly prove that the T-functor can only decrease the embedding dimension in the category of unstable algebras over the Steenrod algebra. As a corollary we obtain that the T-functor preserves the hypersurfaces in the category of unstable algebras. Then with the applications of these results to invariant theory, we also get that if the invariant of a ?nite group is a hypersurface, then so are its stabilizer subgroups. Moreover, by several counter-examples we demonstrate that if the invariants of the stabilizer subgroups or Sylow p-subgroups are hypersurfaces, the invariant of the group itself is not necessarily a hypersurface.
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