Related papers: A proof of Higgins' conjecture

Let G be a finitely presented group, and let {G_i} be a collection of finite index normal subgroups that is closed under intersections. Then, we prove that at least one of the following must hold: 1. G_i is an amalgamated free product or…

We use a hocolim approach to the Isomorphism Conjecture in K-Theory to analyze the case of groups of the form $G\rtimes Z$ and $G_1*_{G}G_2$. As an important corollary we prove that the isomorphism conjecture in K-Theory holds for a…

We show that, if there exists a realization of a Hopf algebra $H$ in a $H$-module algebra $A$, then one can split their cross-product into the tensor product algebra of $A$ itself with a subalgebra isomorphic to $H$ and commuting with $A$.…

A remarkable result of Thompson states that a finite group is soluble if and only if its two-generated subgroups are soluble. This result has been generalized in numerous ways, and it is in the core of a wide area of research in the theory…

The interpolated free group factors L(F_r), 1 < r <= \infty, are defined and proofs of their properties with respect to compression by projections and taking free products are proved. Hence it follows that all the free group factor are…

Bergman has given the following abstract characterisation of the inner automorphisms of a group $G$: they are exactly those automorphisms of $G$ which can be extended functorially along any homomorphism $G \rightarrow H$ to an automorphism…

Given a group $G$, we write $x^G$ for the conjugacy class of $G$ containing the element $x$. A famous theorem of B. H. Neumann states that if $G$ is a group in which all conjugacy classes are finite with bounded size, then the derived group…

We prove the following theorem. Let $G$ be a finite group generated by unitary reflections in a complex Hermitian space $V=\mathbb{C}^\ell$ and let $G'$ be any reflection subgroup of $G$. Let $\mathcal{H}(G)$ be the space of $G$-harmonic…

Building upon previous results, a classification is given of finite $p$-groups of which subgroups of order $p$ are all fused. This completes the classification problem dated back to Higman 1963 on the so-called Suzuki $2$-groups, and…

Howie and Duncan observed that a word in a free product with length at least two and which is not a proper power can be decomposed as a product of two cyclic subwords each of which is uniquely positioned. Using this property, they proved…

We describe (in a representation theoretic setting) a simple comparison of trace formulas, which implies that the conjugate of a Hilbert modular form $f$ by an automorphism of ${\Bbb C}$ again is a Hilbert modular form of the same level and…

In this paper we introduce a new family of icc groups $\Gamma$ which satisfy the following product rigidity phenomenon, discovered in [DHI16] (see also [dSP17]): all tensor product decompositions of the II$_1$ factor $L(\Gamma)$ arise only…

We prove that if $\rho: A(H) \to B(G)$ is a homomorphism between the Fourier algebra of a locally compact group $H$ and the Fourier-Stieltjes algebra of a locally compact group $G$ induced by a mixed piecewise affine map $\alpha : G \to H$,…

Let $\Gamma$ be a finite graph, and for each vertex $i$ let $G_i$ be a finitely presented group. Let $G$ be the graph product of the $G_i$. That is, $G$ is the group obtained from the free product of the $G_i$ by factoring out by the…

We prove a modified version for a conjecture of Weiss from 2004. Let $G$ be a semisimple real algebraic group defined over $\mathbb{Q}$, $\Gamma$ be an arithmetic subgroup of $G$. A trajectory in $G/\Gamma$ is divergent if eventually it…

In this note we prove that the set of all uniformly continuous units on a product system over a C* algebra B can be endowed with the structure of left right B - B Hilbert module after identifying similar units by the suitable equivalence…

The Product Conjecture for the homological Bieri-Neumann-Strebel-Renz invariants is proved over a field. Under certain hypotheses the Product Conjecture is shown to also hold over Z, even though D. Schuetz has recently shown that the…

In this note we prove the following theorem: Let $G$ be a compact Lie group acting on a compact symplectic manifold $M$ in a Hamiltonian fashion. If $L$ is an $l$-dimensional closed invariant submanifold of $M$, on which the $G$-action is…

We prove in ZFC that if $G$ is a (right) $R$-module such that the groups $\Hom_R(\prod_{i\in I}G_i,G)$ and $\prod_{i\in I}\Hom_R(G_i,G)$ are naturally isomorphic for all families of $R$-modules $(G_i)_{i\in I}$ then G=0. The result is valid…

A finitely presented group F is called flawed if Hom(F,G)//G deformation retracts onto its subspace Hom(F,K)/K for reductive affine algebraic groups G and maximal compact subgroups K in G. After discussing generalities concerning flawed…