Abstract In this paper, we show that every irreducible 2-dimensional Artin group $$A_{\Gamma }$$ AΓ of rank at least 3 is acylindrically hyperbolic. We do by studying the action $$A_\Gamma $$ on its modified Deligne complex. Along way, prove results independent interests ge...

It is shown that the compressed word problem of a graph product of finitely generated groups is polynomial time Turing-reducible to the compressed word problems of the vertex groups. A direct corollary of this result is that the word problem for the automorphism group of a right-angled Artin group or a right-angled Coxeter group can be solved in polynomial time. Moreover, it is shown that a res...

Given a group G and an automorphism ? of G, two elements x,y?G are said to be ?-conjugate if x=gy?(g)?1 for some g?G. The number equivalence classes is the Reidemeister R(?) ?, R(?)=? all automorphisms then have R?-property. A finite simple graph ? gives rise right-angled Artin A?, which has as generators vertices relations vw=wv only v w joined by edge in ?. We conjecture that non-abelian grou...

For a local field of characteristic p > 0, K, the combination of local class field theory and Artin-Schreier-Witt theory yield what is known as the Schmid-Witt symbol. The symbol encodes interesting data about the ramification theory of p-extensions of K and we can, for example, use it to compute the higher ramification groups of such extensions. In 1936, Schmid discovered an explicit formula f...