Related papers: Groups generated by two twists along spherical seq…
The group of 2-by-2 matrices with integer entries and determinant $\pm > 1$ can be identified either with the group of outer automorphisms of a rank two free group or with the group of isotopy classes of homeomorphisms of a 2-dimensional…
The group isomorphism problem asks whether two given groups are isomorphic or not. Whereas the case where both groups are abelian is well understood and can be solved efficiently, very little is known about the complexity of isomorphism…
We obtain a classification of the finite two-generated cyclic-by-abelian groups of prime-power order. For that we associate to each such group $G$ a list $\inv(G)$ of numerical group invariants which determines the isomorphism type of $G$.…
We carry out a study of groups $G$ in which the index of any infinite subgroup is finite. We call them restricted-finite groups and characterize finitely generated not torsion restricted-finite groups. We show that every infinite…
Let Gamma be a group generated by two positive multi-twists. We give some sufficient conditions for Gamma to be free or have no `unexpectedly reducible' elements. For a group Gamma generated by two Dehn twists, we classify the elements in…
Finite-dimensional square-free algebras have been completely characterized by Anderson and D'Ambrosia as certain twisted semigroup algebras over a square-free semigroup S with coefficients in a field K. D'Ambrosia extended the definition of…
We obtain explicit formulas for the number of non-isomorphic elliptic curves with a given group structure (considered as an abstract abelian group). Moreover, we give explicit formulas for the number of distinct group structures of all…
The group isomorphism problem asks whether two finite groups given by their Cayley tables are isomorphic or not. Although there are polynomial-time algorithms for some specific group classes, the best known algorithm for testing isomorphism…
We give an algorithm to decide if a given braid is a product of two factors which are conjugates of given powers of standard generators of the braid group. The same problem is solved in a certain class of Garside groups including Artin-Tits…
Frucht showed that, for any finite group $G$, there exists a cubic graph such that its automorphism group is isomorphic to $G$. For groups generated by two elements we simplify his construction to a graph with fewer nodes. In the general…
We describe the two-generated limits of abelian-by-(infinite cyclic) groups in the space of marked groups using number theoretic methods. We also discuss universal equivalence of these limits.
The strong isomorphism classes of extensions of finite groups are parametrized by orbits of a prescribed action on the second cohomology group. We study these orbits in the case of extensions of a finite abelian $p$-group by a cyclic factor…
We show that the morphisms from the braid group with n strands in the mapping class group of a surface with a possible non empty boundary, assuming that its genus is smaller or equal to n/2 are either cyclic morphisms (their images are…
Isotopy classes of diffeomorphisms of the 4-sphere can be described either from a Cerf theoretic perspective in terms of loops of 5-dimensional handle attaching data, starting and ending with handles in cancelling position, or via certain…
If we have a braid group acting on a derived category by spherical twists, how does a lift of the longest element of the symmetric group act? We give an answer to this question, using periodic twists, for the derived category of modules…
A $T$-Schottky group is a discrete group of M\"obius transformations whose generators identify pairs of, possibly-tangent, Jordan curves on the complex sphere, ${\hat{\IC}}$. If the curves are Euclidean circles then the group is termed…
We show that on an arbitrary finitely generated non virtually solvable linear group, any two independent random walks will eventually generate a free subgroup. In fact, this will hold for an exponential number of independent random walks.
We construct spherical subgroups in infinite-dimensional classical groups $G$ (usually they are not symmetric and their finite-dimensional analogs are not spherical). We present a structure of a semigroup on double cosets $L\setminus G/L$…
The Addition Theorem for the algebraic entropy of group endomorphisms of torsion abelian groups was proved in [4]. Later, this result was extended to all abelian groups [3] and, recently, to all torsion finitely quasihamiltonian groups [7].…
We prove that each infinite 2-group with a unique 2-element subgroup is isomorphic either to the quasicyclic 2-group or to the infinite group of generalized quaternions.