Fast searching for Andrews-Curtis trivializations.
Finite geometry for a generation.
Finite groups in which every two elements generate a soluble subgroup.
Finite presentations for the mapping class group via the ordered complex of curves.
Finite representations of pro-p groups and discrete groups.
Finite sets and symmetric simplicial sets.
Finite simple groups of Lie type as expanders
We prove that all finite simple groups of Lie type, with the exception of the Suzuki groups, can be made into a family of expanders in a uniform way. This confirms a conjecture of Babai, Kantor and Lubotzky from 1989, which has already been proved by Kassabov for sufficiently large rank. The bounded rank case is deduced here from a uniform result for which is obtained by combining results of Selberg and Drinfeld via an explicit construction of Ramanujan graphs by Lubotzky, Samuels and Vishne.
Finite tangled groups.
Finitely generated groups having a finite set of conjugacy classes meeting all cyclic subgroups
We study infinite finitely generated groups having a finite set of conjugacy classes meeting all cyclic subgroups. The results concern growth and the ascending chain condition for such groups.
Finitely Generated pro-2 Groups with a free subgroup of Index 2.
Finitely generated soluble groups with an Engel condition on infinite subsets
First Order Classes of Groups Having no Groups With a Given Property
First-order definability and algebraicity of the sets of annihilating and generating collections of elements for some relatively free solvable groups.
Følner sequences in polycyclic groups.
The isoperimetric inequality |∂Ω| / |Ω| = constant / log |Ω| for finite subsets Ω in a finitely generated group Γ with exponential growth is optimal if Γ is polycyclic.
Formal language theory and the geometry of 3-manifolds.
Framed Links for Pfeiffer Identities.
Free and non-free subgroups of the fundamental group of the Hawaiian Earrings
The space which is composed by embedding countably many circles in such a way into the plane that their radii are given by a null-sequence and that they all have a common tangent point is called “The Hawaiian Earrings”. The fundamental group of this space is known to be a subgroup of the inverse limit of the finitely generated free groups, and it is known to be not free. Within the recent move of trying to get hands on the algebraic invariants of non-tame (e.g. non-triangulable) spaces this space...
Free quotients of finitely presented groups.
Frobenius groups generated by two elements of order 3.
Fundamental central dispersion in a simple system