Lanne’s T-functor and Hypersurfaces
Received:September 17, 2016  Revised:August 20, 2017
Key Word: T-functor, Hypersurface, Pointwise stabilizers  
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Author NameAffiliationE-mail
Zheng Wenhua School of Mathematical Science, Dalian University of Technology 
Nan Jizhu School of mathematical science, Dalian Universtiy of Technology 
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      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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