Power linear Keller maps of dimension three

Power Linear Keller Maps of Dimension Three

In this paper it is proved that a power linear Keller map of dimension three over a field of characteristic zero is linearly triangularizable. Let K be a field. A polynomial map F in dimension n over K is an n-tuple (F1, F2, · · · , Fn) of polynomials in K[X1, X2, · · · , Xn]. If G is another polynomial map of the same dimension, then the composition of F and G is defined by F ◦G = (F1(G1, G2, ...

Irreducibility properties of Keller maps

J ‘ edrzejewicz showed that a polynomial map over a field of characteristic zero is invertible, if and only if the corresponding endomorphism maps irreducible polynomials to irreducible polynomials. Furthermore, he showed that a polynomial map over a field of characteristic zero is a Keller map, if and only if the corresponding endomorphism maps irreducible polynomials to square-free polynomial...

On the Restriction of Characters of Special Linear Groups of Dimension Three

The Jacobian Conjecture: linear triangularization for homogeneous polynomial maps in dimension three

Let k be a field of characteristic zero and F : k → k a polynomial map of the form F = x + H, where H is homogeneous of degree d ≥ 2. We show that the Jacobian Conjecture is true for such mappings. More precisely, we show that if JH is nilpotent there exists an invertible linear map T such that T−1HT = (0, h2(x1), h3(x1, x2)), where the hi are homogeneous of degree d. As a consequence of this r...

Characterization of projective special linear groups in dimension three by their orders and degree patterns

The prime graph $Gamma(G)$ of a group $G$ is a graph with vertex set $pi(G)$, the set of primes dividing the order of $G$, and two distinct vertices $p$ and $q$ are adjacent by an edge written $psim q$ if there is an element in $G$ of order $pq$. Let $pi(G)={p_{1},p_{2},...,p_{k}}$. For $pinpi(G)$, set $deg(p):=|{q inpi(G)| psim q}|$, which is called the degree of $p$. We also set $D(G):...