City College of New York

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19922026

most citedExperimental and Theoretical Challenges in the Search for the Quark Gluon Plasma: The STAR Collaboration's Critical Assessment of the Evidence from RHIC Collisions

3.4k citations

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Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.

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74 papers · 1 filter

math.GR2025

Two-sided homological properties of special and one-relator monoids

Robert D. Gray, Benjamin Steinberg

A monoid presentation is called special if the right-hand side of each defining relation is equal to 1. We prove results which relate the two-sided homological finiteness propertie…

math.GR2023

On isomorphisms to a free group and beyond

Vladimir Shpilrain

The isomorphism problem for infinite finitely presented groups is probably the hardest among standard algorithmic problems in group theory. Classes of groups where it has been comp…

math.GR2018★ 3 cited

Commensurability growth of branch groups

Khalid Bou-Rabee, Rachel Skipper, Daniel Studenmund

Fixing a subgroup $Γ$ in a group $G$ , the commensurability growth function assigns to each $n$ the cardinality of the set of subgroups $Δ$ of $G$ with $[Γ: Γ\cap Δ][Δ: Γ\cap Δ] = n…

math.GR2018★ 1 cited

Pointlike sets for varieties determined by groups

Samuel J. v. Gool, B. Steinberg

For a variety of finite groups $H$ , let $H$ denote the variety of finite semigroups all of whose subgroups lie in $H$ . We give a characterization…

math.GR2017

The Extrinsic Primitive Torsion Problem

Khalid Bou-Rabee, W. Patrick Hooper

Let $P_{k}$ be the subgroup generated by $k$ th powers of primitive elements in $F_{r}$ , the free group of rank $r$ . We show that $F_{2} / P_{k}$ is finite if and only if $k$ is $1$ , $2$ , or…

math.GR2017★ 5 cited

Topological finiteness properties of monoids. Part 1: Foundations

Robert D. Gray, Benjamin Steinberg

We initiate the study of higher dimensional topological finiteness properties of monoids. This is done by developing the theory of monoids acting on CW complexes. For this we estab…

math.GR2016

Expected Depth of Random Walks on Groups

Khalid bou-Rabee, Ioan Manolescu, Aglaia Myropolska

For $G$ a finitely generated group and $g \in G$ , we say $g$ is detected by a normal subgroup $N ⊲ G$ if $g \in / N$ . The depth $D_{G} (g)$ of $g$ is the lowest index of a normal,…

math.GR2016★ 2 cited

On two-generator subgroups in SL_2(Z), SL_2(Q), and SL_2(R)

Anastasiia Chorna, Katherine Geller, Vladimir Shpilrain

We consider what some authors call 'parabolic Möbius subgroups' of matrices over Z, Q, and R and focus on the membership problem in these subgroups and complexity of relevant algor…

math.GR2016

On the atoms of algebraic lattices arising in $q$ -theory

Attila Egri-Nagy, Marcel Jackson, John Rhodes +1

We determine many of the atoms of the algebraic lattices arising in $q$ -theory of finite semigroups.

math.GR2015★ 59 cited

Between primitive and $2$ -transitive: Synchronization and its friends

João Araújo, Peter J. Cameron, Benjamin Steinberg

An automaton is said to be synchronizing if there is a word in the transitions which sends all states of the automaton to a single state. Research on this topic has been driven by…

math.GR2015★ 3 cited

The pro-nilpotent group topology on a free group

J. Almeida, M. H. Shahzamanian, B. Steinberg

In this paper, we work on the pro-nilpotent group topology of a free group. First we investigate the closure of the product of finitely many subgroups of a free group in the pro-ni…

math.GR2015★ 8 cited

Weakly maximal subgroups in regular branch groups

Khalid Bou-Rabee, Paul-Henry Leemann, Tatiana Nagnibeda

Let $G$ be a finitely generated regular branch group acting by automorphisms on a regular rooted tree $T$ . It is well-known that stabilizers of infinite rays in $T$ (aka parabolic…

math.GR2014

Navigating in the Cayley graph of $S L_{2} (F_{p})$ and applications to hashing

Lisa Bromberg, Vladimir Shpilrain, Alina Vdovina

Cayley hash functions are based on a simple idea of using a pair of (semi)group elements, $A$ and $B$ , to hash the 0 and 1 bit, respectively, and then to hash an arbitrary bit stri…

math.GR2014★ 6 cited

Systolic growth of linear groups

Khalid Bou-Rabee, Yves Cornulier

We prove that the residual girth of any finitely generated linear group is at most exponential. This means that the smallest finite quotient in which the $n$ -ball injects has at mo…

math.GR2014★ 5 cited

Full residual finiteness growths of nilpotent groups

Khalid Bou-Rabee, Daniel Studenmund

Full residual finiteness growth of a finitely generated group $G$ measures how efficiently word metric $n$ -balls of $G$ inject into finite quotients of $G$ . We initiate a study of…

math.GR2014★ 5 cited

Characterizing linear groups in terms of growth properties

Khalid Bou-Rabee, D. B. McReynolds

Residual finiteness growth measures how well-approximated a group is by its finite quotients. We prove that some related growth functions characterize linearity for a class of grou…

math.GR2014★ 7 cited

Commensurations and Metric Properties of Houghton's Groups

José Burillo, Sean Cleary, Armando Martino +1

We describe the automorphism groups and the abstract commensurators of Houghton's groups. Then we give sharp estimates for the word metric of these groups and deduce that the comme…

math.GR2014

Obstructions for subgroups of Thompson's group $V$

José Burillo, Sean Cleary, Claas E. Röver

Thompson's group $V$ has a rich variety of subgroups, containing all finite groups, all finitely generated free groups and all finitely generated abelian groups, the finitary permu…

math.GR2014★ 13 cited

Residual Finiteness Growths of Virtually Special Groups

Khalid Bou-Rabee, Mark F. Hagen, Priyam Patel

Let $G$ be a virtually special group. Then the residual finiteness growth of $G$ is at most linear. This result cannot be found by embedding $G$ into a special linear group. Indeed…

math.GR2013★ 3 cited

Rational Subsets and Submonoids of Wreath Products

Markus Lohrey, Benjamin Steinberg, Georg Zetzsche

It is shown that membership in rational subsets of wreath products H \wr V with H a finite group and V a virtually free group is decidable. On the other hand, it is shown that ther…

math.GR2013

Addendum to "Commensurations and Subgroups of Finite Index of Thompson's Group F"

José Burillo, Sean Cleary, Claas E. Röver

We show that the abstract commensurator of Thompson's group F is composed of four building blocks: two isomorphism types of simple groups, the multiplicative group of the positive…

math.GR2012★ 1 cited

Semigroups embeddable in hyperplane face monoids

Stuart Margolis, Franco Saliola, Benjamin Steinberg

The left regular band structure on a hyperplane arrangement and its representation theory provide an important connection between semigroup theory and algebraic combinatorics. A fi…

math.GR2011

The Krohn-Rhodes Theorem and Local Divisors

Volker Diekert, Manfred Kufleitner, Benjamin Steinberg

We give a new proof of the Krohn-Rhodes Theorem using local divisors. The proof provides nearly as good a decomposition in terms of size as the holonomy decomposition of Eilenberg,…