Coinvariants and the regular representation of a cyclic \(P\)-group
type: Item
instance of: scholarly article
title: Coinvariants and the regular representation of a cyclic \(P\)-group
zbMATH Open document ID: 1266.13004
author: Müfit Sezer
published in: Mathematische Zeitschrift
publication date: 2013-02-06T00:00:00Z
review text: Let \(p > 0\) be a prime number and let \(F\) be a field of characteristic \(p\). Let \(V\) be a finite dimensional representation of a finite group \(G\) over \(F\). \(F[V]\) denotes the ring of polynomial functions on \(V\), and the ring of invariant polynomials \(F\left[V \right]^G = \left\{f\in F\left[V \right] |g\left(f\right) = f \forall g \in G\right\}\), which is a graded, finitely generated subalgebra of \(F\left[V \right]\). The author of this article considered an indecomposable representation of the cyclic p-group \(G = \mathbb Z_{p^r}\) over a field \(F\) of characteristic \(p\). He showed that the top degree of the corresponding ring of coinvariants is less than \(\frac{(r^2+3r)p^r}{2}\). This bound also applies to the degrees of the generators for the invariant ring of the regular representation.
reviewed by: Jebrel M. Habeb
Mathematics Subject Classification ID: 13A50
Mathematics Subject Classification ID: 14L24
zbMATH DE Number: 6134693
zbMATH Keywords: coinvariants
zbMATH Keywords: modular cyclic groups
zbMATH Keywords: degree bounds
MaRDI profile type: Publication
full work available at URL: s00209-012-1018-8
OpenAlex ID: W2124169153
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DOI: 10.1007/S00209-012-1018-8
description: scientific article; zbMATH DE number 6134693