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We provide an explicit presentation of an infinite hyperbolic Kazhdan group with $4$ generators and $16$ relators of length at most $73$. That group acts properly and cocompactly on a hyperbolic triangle building of type $(3,4,4)$. We also point out a variation of the construction that yields examples of lattices in $tilde A_2$-buildings admitting non-Desarguesian residues of arbitrary prime power order.
Let $G$ be an acylindrically hyperbolic group on a $delta$-hyperbolic space $X$. Assume there exists $M$ such that for any generating set $S$ of $G$, $S^M$ contains a hyperbolic element on $X$. Suppose that $G$ is equationally Noetherian. Then we sho
For a tuple $A=(A_1, A_2, ..., A_n)$ of elements in a unital Banach algebra ${mathcal B}$, its {em projective joint spectrum} $P(A)$ is the collection of $zin {mathbb C}^n$ such that the multiparameter pencil $A(z)=z_1A_1+z_2A_2+cdots +z_nA_n$ is not
In this paper, we generalise Magnus Freiheitssatz and solution to the word problem for one-relator groups by considering one relator quotients of certain classes of right-angled Artin groups and graph products of locally indicable polycyclic groups.
In this article we produce an example of a non-residually finite group which admits a uniformly proper action on a Gromov hyperbolic space.
We prove a freeness theorem for low-rank subgroups of one-relator groups. Let $F$ be a free group, and let $win F$ be a non-primitive element. The primitivity rank of $w$, $pi(w)$, is the smallest rank of a subgroup of $F$ containing $w$ as an imprim