Related papers: Torsion elements in branch pro-$p$ groups

In this note we prove that there is no constant $C$, depending on the genus of the surface, such that every element in the mapping class group can be written as a product of at most $C$ torsion elements, answering a question of T. E.…

The authors have shown previously that every locally pro-p contraction group decomposes into the direct product of a p-adic analytic factor and a torsion factor. It has long been known that p-adic analytic contraction groups are nilpotent.…

Using the division polynomials for elliptic curves in Weierstrass form, it shown that the group of rational points on the curve $H: ky(yy - 1) = lx(xx - 1)$ is torsion-free.

In [9] we proved that the space of countable torsion-free abelian groups is Borel complete. In this paper we show that our construction from [9] satisfies several additional properties of interest. We deduce from this that countable…

We provide a short proof that the dimensions of the mod $p$ homology groups of the unordered configuration space $B_k(T)$ of $k$ points in a torus are the same as its Betti numbers for $p>2$ and $k\leq p$. Hence the integral homology has no…

Let A be a commutative noetherian ring. Call a functor <<commutative A-algebras>> --> <<sets>> coherent if it can be built up (via iterated finite limits) from functors of the form B \mapsto M tensor_A B, where M is a f.g. A-module. When…

Let $E$ be an elliptic curve over a quartic field $K$. By the Mordell-Weil theorem, $E(K)$ is a finitely generated group. We determine all the possibilities for the torsion group $E(K)_{tor}$ where $K$ ranges over all quartic fields $K$ and…

Let p be a prime. A p-adic functional on a torsion-free abelian group G is a group homomorphism from G to the p-adic integers. The group of all such p-adic functionals is viewed as a p-adic dual group of G, and is studied from the point of…

We examine the first non-vanishing higher homotopy group, $\pi_p$, of the complement of a hypersolvable, non--supersolvable, complex hyperplane arrangement, as a module over the group ring of the fundamental group, $\Z\pi_1$. We give a…

A pro-p Cappitt group is a pro-p group G such that the subgroup topologically generated by all non-normal closed subgroups is a proper subgroup of G. In this paper we prove that non-abelian pro-p Cappitt groups whose torsion subgroup is…

Under the assumption that Galois representations associated to Siegel modular forms exist (it is known only for genus at most 2), we show that the cohomology with p-adic integral coefficients of Siegel Varieties, when localized at a…

We find a necessary condition for zero divisors in complex group algebras of torsion-free groups.

Let $p$ and $q$ be multiplicatively independent integers. We show that the complex group ring of $\mathbb{Z}[\frac{1}{pq}]\rtimes\mathbb{Z}^2$ admits a unique $\mathrm{C}^*$-norm. The proof uses a characterization, due to Furstenberg, of…

Let p be a prime. Uniform pro-p groups play a central role in the theory of p-adic Lie groups. Indeed, a topological group admits the structure of a p-adic Lie group if and only if it contains an open pro-p subgroup which is uniform.…

We prove that the $p^\infty$-torsion of the transcendental Brauer group of an abelian variety over a finitely generated field of characteristic $p>0$ is bounded. This answers a (variant of a) question asked by Skorobogatov and Zarhin for…

In this article, we study the log-scheme theoretic version of the Nori fundamental group scheme. Similar to the classical Nori fundamental group scheme, the log Nori fundamental group scheme classifies torsors on log flat topology. We also…

We show, for a smooth projective variety $X$ over an algebraically closed field $k$ with an effective Cartier divisor $D$, that the torsion subgroup $\CH_0(X|D)\{l\}$ can be described in terms of a relative {\'e}tale cohomology for any…

We study the torsion free generalized crystallographic groups with the indecomposable holonomy group which is isomorphic to either a cyclic group of order ${p^s}$ or a direct product of two cyclic groups of order ${p}$.

For any field $\mathbb{F}$ and all torison-free group $\mathbb{G}$, we prove that if $ab = 0$ for some non-zero $a, b \in \mathbb{F}[\mathbb{G}]$ such that $|supp(a)|$ $= 3$ and $a = 1 + \alpha_{1}g_{1} + \alpha_{2}g_{2}$, then $g_{1},…

Let $X$ be a smooth projective quadric defined over a field of characteristic 2. We prove that in the Chow group of codimension 2 or 3 of $X$ the torsion subgroup has at most two elements. In codimension 2, we determine precisely when this…