First Author: Dave Benson
email: /b\e/n\s/o\n/d\j (without the slashes) at math dot uga dot edu
Address:
Department of Mathematics,
University of Georgia
Second Author: Peter Webb
email: webb@math.umn.edu
Address:
School of Mathematics,
University of Minnesota,
Minneapolis MN 55455
Title:
Unique factorization in invariant power series rings
Abstract:
Let G be a finite group, k a perfect field of characteristic p,
and Va finite dimensional kG-module.
We let G act on the power series k[[V]] by linear substitutions
and address the question of when the invariant
power series k[[V]]^G form a unique factorization domain. We prove
that for a permutation module for a p-group, the answer is always
positive. On the other hand, if G is a cyclic group of order p
and V is an indecomposable kG-module of dimension r with
1 \le r \le p, we show that the invariant
power series form a unique factorization domain if and only if
r is equal to 1, 2, p-1 or p. This contradicts a conjecture
of Peskin.
Preprint: April 2005.
Updated: January 2006