Nilpotence in groups of semi linear maps III

Realization of a Certain Class of Semi-Groups as Value Semi-Groups of Valuations

A Testing Nilpotence of Galois Groups in Polynomial Time

We give the first polynomial-time algorithm for checking whether the Galois group Gal (f) of an input polynomial f(X) ∈ Q[X] is nilpotent: the running time of our algorithm is bounded by a polynomial in the size of the coefficients of f and the degree of f . Additionally, we give a deterministic polynomial-time algorithm that, when given as input a polynomial f(X) ∈ Q[X] with nilpotent Galois g...

Brauer pairs of Camina p - groups of nilpotence class 2

In this paper, we find a condition that characterizes when two Camina p-groups of nilpotence class 2 form a Brauer pair. MSC primary: 20C15

Residual Nilpotence for Generalizations of Pure Braid Groups

It is known that the pure braid groups are residually torsion-free nilpotent. This property is however widely open for the most obvious generalizations of these groups, like pure Artin groups and like fundamental groups of hyperplane complements (even reflection ones). In this paper we relate this problem to the faithfulness of linear representations, and prove the residual torsion-free nilpote...

A Note on The Local Nilpotence of 4-Engel Groups

Recently Havas and Vaughan-Lee proved that 4-Engel groups are locally nilpotent. Their proof relies on the fact that a certain 4-Engel group T is nilpotent and this they prove using a computer and the Knuth-Bendix algorithm. In this paper we give a short hand-proof of the nilpotency of T .