72 papers
This paper derives exact formulas for the proportions of derangements and derangements of -power order in various affine classical groups, utilizing a new generating function for specific integer partitions in the unitary case and verifying -polynomial identities in the symplectic and orthogonal cases.
This paper establishes that a commutator is a -element for all if and only if is central modulo , a result that generalizes the Baer--Suzuki and Glauberman -theorems and is applied to prove that a conjugacy class satisfying generates a solvable subgroup.
This paper introduces the concept of strongly -inverse monoids, provides a presentation for the universal -generated strongly -inverse monoid with a given maximum group image, and applies this framework to fully characterize one-relator special inverse monoids with cyclically reduced relators that possess this property.
This paper proves that finite groups with semidihedral Sylow 2-subgroups possess a class-preserving Coleman outer automorphism group of odd order, thereby confirming that these groups satisfy the normalizer problem and extending existing results in the field.
This paper establishes the non-amenability of mapping class groups for infinite-type surfaces and locally finite infinite graphs of higher ranks, provides an example of a non-amenable point stabilizer in a specific hyperbolic Polish group, and identifies a class of amenable mapping class groups associated with trees and rank-one graphs.
This paper introduces new finite criteria that enable a practical algorithm to certify projective Anosov subgroups in or , significantly reducing the computational complexity required for verification as demonstrated by a genus 2 surface group example.
This paper establishes that convex-cocompact representations of finitely generated groups into the isometry group of infinite-dimensional hyperbolic space form an open set, enabling the construction of new surface group representations via bending that are distinct from those classified by Monod and Py.
This paper characterizes the amenability of countable Borel equivalence relations via the uniform Liouville property, investigates Kesten's property for return probabilities on topological groups, and constructs an amenable contractible Polish group lacking this property by linking it to anti-concentration inequalities in measurable lamplighter groups.
This paper establishes that the explorability of a finitely generated group's Cayley graph by finite automata systems depends on the group's periodicity: periodic groups confine automata to finite areas, groups with non-periodic elements are explorable by automata with three pebbles, and aperiodic groups cannot be explored by any finite automata system.
This paper investigates bona fide context-free trees by demonstrating their finite-state description via multi-edge NFAs and proving that the isomorphism problem for deterministic context-free trees is NL-complete in both rooted and non-rooted cases.
This paper proves that every large connected Cayley graph with degree at least for some absolute constant contains a Hamilton cycle, thereby advancing the Lovász conjecture by improving previous density thresholds through a proof that utilizes an arithmetic regularity lemma tailored to Cayley graphs instead of Szemerédi's regularity lemma.
This paper investigates the growth rates, asymptotic behaviors, and Gauss congruences of Reidemeister and Nielsen coincidence numbers for endomorphisms of torsion-free nilpotent groups and maps on compact nilmanifolds, while also establishing the rationality of the Nielsen coincidence zeta function.
This paper classifies unital cubic maps from the cyclic group of order 3 into arbitrary non-abelian groups, demonstrating that the associated universal group is an infinite arithmetic lattice in and establishing the existence of finite nilpotent groups of arbitrarily large nilpotency class admitting such maps.
This paper proves that as approaches infinity, the proportion of orientably-regular maps and hypermaps with automorphism groups or that are chiral tends to 1, establishing that chirality is generic for these structures.
This paper investigates the irreducible components of fixed point sets within the -character variety of a genus two surface under finite group actions, utilizing the genus two DAHA to identify geometric transitions that yield novel candidates for symmetry-reduced moduli spaces in 4d SCFTs.
This paper partially answers Genevois's question regarding when hyperbolic graph braid groups arise as 3-manifold groups by demonstrating that is a 3-manifold group while for is not even quasi-isometric to one.
This paper characterizes the fundamental group of disjointly tree-graded spaces in terms of the fundamental groups of their constituent pieces, establishing an embedding into an inverse limit of free products even when local simple connectivity is absent.
This paper generalizes the Peter-Weyl Theorem by demonstrating that functions on locally compact groups with large nontrivial compact open subgroups can be approximated by locally representative functions.
This paper provides a comprehensive survey of various Waring-type problems across the mathematical structures of groups, Lie algebras, and associative algebras.
This paper proposes weaker constraints on filters for group convolutional neural networks that reduce the required number of nodes while resolving incompatibilities with non-compact stabilizers and generalizing results to non-transitive group actions and non-unimodular groups.