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Proceedings of the American Mathematical Society

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The Steenrod algebra action on generators of rings of invariants of subgroups of $ {\rm GL}\sb n({\bf Z}/p{\bf Z})$


Author: Nondas E. Kechagias
Journal: Proc. Amer. Math. Soc. 118 (1993), 943-952
MSC: Primary 55S10
DOI: https://doi.org/10.1090/S0002-9939-1993-1152986-4
MathSciNet review: 1152986
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Abstract: We compute the action of the Steenrod algebra on rings of invariants of certain subgroups of $ {\operatorname{GL} _n}({\mathbf{Z}}/p{\mathbf{Z}})$, namely, the upper triangular and parabolic subgroups. As a consequence we get the action on the Dickson algebra for any prime $ p$. The methods we use are elementary.


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DOI: https://doi.org/10.1090/S0002-9939-1993-1152986-4
Keywords: Modular invariants, Steenrod operations
Article copyright: © Copyright 1993 American Mathematical Society