Trace form preservers (Q1300863)

Let \(K\) be a field, \(X\) the set of \(n\times n\) matrices over the field, and \(T^d(X)= \text{tr}(x^d)\). A field of characteristic \(p\) with \(|K|> d>2\) is considered. If \(d\) is not of the form \(p^m\) or \(2p^m\), then every preserver of \(T^d\) is \(\lambda\)-standard. The cases of large fields and small fields are discussed separately.