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On degree bounds for separating invariants | Martin Kohls
; | Date: |
28 Jan 2010 | Abstract: | Let a group $G$ act on a finite dimensional vector space $V$ over an
algebraically closed field $K$ of characteristic $p$. Then $eta_{sep}(G)$ is
the minimal number such that, for any $V$, the invariants of degree less or
equal than this number have the same separating properties as the whole
invariant ring $K[V]^{G}$. Derksen and Kemper have shown $eta_{sep}(G)le
|G|$. We show $eta_{sep}(G)=|G|$ for $p$-groups and cyclic groups, and
$eta_{sep}(G)=infty$ for infinite unipotent groups. We also show
$eta_{sep}(G)le eta_{sep}(G/N)eta_{sep}(N)$ for a normal divisor $N$
of finite index. | Source: | arXiv, 1001.5216 | Services: | Forum | Review | PDF | Favorites |
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