The Direct Summand Property in Modular Invariant Theory |
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Authors: | Abraham Broer |
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Institution: | (1) Departement de mathematiques et de statistique, Universite de Montreal, C.P. 6128, succursale Centre-ville, Montreal (Quebec) H3C 3J7, Canada |
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Abstract: | In nonmodular invariant theory of finite groups, the
invariant ring is always a direct summand of the full
polynomial ring. This is no longer generally true in
modular invariant theory, but nevertheless interesting
examples are known where this happens. We give useful
characterisations of the direct summand property in terms
of the image of a twisted transfer map. For example, for
p-groups acting in characteristic p the direct summand
property holds if and only if the image of the ordinary
transfer is a principal ideal; and in that case the group
is generated by transvections. We also extend some known
results in the nonmodular case to where only the direct
summand property is assumed, e.g., the invariant ring is
always generated by its elements of degree at most the
order of the group. |
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Keywords: | |
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