ℤ n -free groups are CAT(0)

Gaussian Groups Are Torsion Free

Assume that G is a group of fractions of a cancellative monoid where lower common multiples exist and divisibility has no infinite descending chain. Then G is torsion free. The result applies in particular to all finite Coxeter type Artin groups. Finding an elementary proof for the fact that Artin’s braid groups are torsion free has been reported to be a longstanding open question [9]. The exis...

REIDEMEISTER SPECTRUM FOR METABELIAN GROUPS OF THE FORM Q n ⋊ Z AND Z[1/p] n ⋊ Z, p PRIME.

In this note we study the Reidemeister spectrum for metabelian groups of the form Q ⋊Z and Z[1/p]n ⋊Z. Particular attention is given to the R∞ property of a subfamily of these groups.

Commutativity degree of $mathbb{Z}_p$≀$mathbb{Z}_{p^n}

For a nite group G the commutativity degree denote by d(G) and dend:$$d(G) =frac{|{(x; y)|x, yin G,xy = yx}|}{|G|^2}.$$ In [2] authors found commutativity degree for some groups,in this paper we nd commutativity degree for a class of groups that have high nilpontencies.

n-cyclicizer groups

Random Extensions of Free Groups and Surface Groups Are Hyperbolic

In this note, we prove that a random extension of either the free group FN of rank N ě 3 or of the fundamental group of a closed, orientable surface Sg of genus g ě 2 is a hyperbolic group. Here, a random extension is one corresponding to a subgroup of either OutpFN q or ModpSgq generated by k independent random walks. Our main theorem is that a k–generated random subgroup of ModpSgq or OutpFN ...