On the number of indecomposable matrix representations of given degree of a finite \(p\)-group over commutative local rings of characteristic \(p^s\) (Q2759402)

The main results of the article are the following. Let \(G\) be a finite \(p\)-group of order \(|G|>2\), let \(K\) be commutative local ring of characteristic \(p^s\), (\(s\geq 1\)), \(\text{Rad }K\neq 0\) and let \(K/\text{Rad }K\) be an infinite field. Here \(\text{Rad }K\) is the Jacobson radical of the ring \(K\). Then the number of nonequivalent indecomposable matrix \(K\)-representations of arbitrary degree \(n>1\) of the group \(G\) is infinite. If \(G\) is a finite \(p\)-group of order \(|G|>2\), \(K\) is a commutative local integral domain of characteristic \(p\), which is not a field, then the number of nonequivalent indecomposable matrix \(K\)-representations of arbitrary degree \(n>1\) of the group \(G\) is infinite.