Related papers: A finitely generated group that does not satisfy t…
We give an example of a finitely presented simple group containing a finitely generated subgroup which is not finitely presented.
We prove that every finitely generated soluble group which is not virtually abelian has a subgroup of one of a small number of types.
We construct a finitely generated 2-dimensional group that acts properly on a locally finite CAT(0) cube complex but does not act properly on a finite dimensional CAT(0) cube complex.
A finitely generated solvable group with unbounded iterated identity is constructed.
We construct a finitely generated group which is an extension of two finitely generated groups coarsely embeddable into Hilbert space but which itself does not coarsely embed into Hilbert space. Our construction also provides a new infinite…
We prove that there exists a finitely generated group that satisfies a group law with probability 1 but does not satisfy any group law. More precisely, we construct a finitely generated group G in which the probability that a random element…
We study fundamental groups of non compact Riemannian manifolds. We find conditions which ensure that the fundamental group is trivial, finite or finitely generated.
We prove the Burghelea Conjecture for groups satisfying some additional cohomological property.
Let $d \geq 2$ be an integer. We conjecture that there is a finitely generated perfect group whose homomorphic images include all finite $d$-generated perfect groups. We prove a special case of this conjecture for the finite perfect groups…
We review the Burghelea conjecture, which constitutes a full computation of the periodic cyclic homology of complex group rings, and its relation to the algebraic Baum-Connes conjecture. The Burghelea conjecture implies the Bass conjecture.…
We give a structural theorem for pseudofinite groups of finite centraliser dimension. As a corollary, we observe that there is no finitely generated pseudofinite group of finite centraliser dimension.
It is shown that there exists a finitely generated infinite simple group of infinite commutator width, and that the commutator width of a finitely generated infinite boundedly simple group can be arbitrarily large. Besides, such groups can…
It is proven that an infinite finitely generated group cannot be elementarily equivalent to an ultraproduct of finite groups of a given Pr\"ufer rank. Furthermore, it is shown that an infinite finitely generated group of finite Pr\"ufer…
We present two uncountable families of finitely generated residually finite groups all having the same profinite completion. One consists of soluble groups, the other of branch groups.
We construct a finitely presented group $G$ with non-quadratic Dehn function $f$ majorizable by a quadratic function on arbitrary long intervals.
A group is metabelian if its commutator subgroup is abelian. For finitely generated metabelian groups, classical commutative algebra, algebraic geometry and geometric group theory, especially the latter two subjects, can be brought to bear…
We propose a general conjecture on decompositions of finite simple groups as products of conjugates of an arbitrary subset. We prove this conjecture for bounded subsets of arbitrary finite simple groups, and for large subsets of groups of…
Necessary and sufficient conditions for finite commutative semihypergroups to be built from abelian groups of the same order are established.
Motivated by a question of Bumagin and Wise, we construct a continuum of finitely generated, residually finite groups whose outer automorphism groups are pairwise non-isomorphic finitely generated, non-recursively-presentable groups. These…
We construct a finitely generated residually finite group $G$ with the property that every finite index subgroup of $G$ contains a subgroup isomorphic to Promislow's group. Hence $G$ does not have a finite index subgroup with the unique…