The braid groups Bn were originally introduced by Emil Artin in 1926. They have many interpretations, for example, as the group of geometric braids in R, as the Artin group of type An, as the fundamental group of a certain hyperplane arrangement, as a subgroup of the automorphism group of a free group, and so on. In this paper we will use the interpretation of Bn as the mapping class group of a...

The main objects of this paper are the graded automorphisms of w x polytopal semigroup rings, i.e., semigroup rings k S where k is a field P Ž and S is the semigroup associated with a lattice polytope P Bruns, P w x. w x Gubeladze, and Trung BGT . The generators of k S correspond bijecP tively to the lattice points in P, and their relations are the binomials representing the affine dependencies...

We give a summary, without proofs, of basic properties of linear algebraic groups, with particular emphasis on reductive algebraic groups.

We discuss distortion of solvable linear groups over a locally compact field and provide necessary and sufficient conditions for a subgroup to be undistorted when the field is of characteristic zero.

These are the exercises (with solutions) and the exam for the course Algebra II, winter term 2014/2015 at Bonn. Students were not assumed to have heard algebraic geometry before, just algebra. In particular, basic affine and projective geometry were introduced from scratch. The course covered the standard material up to the structure results about maximal tori and Borel subgroups. Root systems ...

Let G be a noncyclic group of order 4, and let K = Z, Z (2) and Z 2 be the ring of rational integers, the localization of Z at the prime 2 and the ring of 2-adic integers, respectively. We describe, up to conjugacy, all of the indecomposable subgroups in the group GL(m, K) which are isomorphic to G. The first explicit description of the Z-representations of the noncyclic group G of order 4 was ...

we discuss whether finiteness properties of a profinite group $g$ can be deduced from the coefficients of the probabilisticzeta function $p_g(s)$. in particular we prove that if $p_g(s)$ is rational and all but finitely many non abelian composition factors of $g$ are isomorphic to $psl(2,p)$ for some prime $p$, then $g$ contains only finitely many maximal subgroups.