Related papers: On the Isomorphism of Some One-Relator Groups

Let G be a group. Two elements x,y are said to be in the same z-class if their centralizers are conjugate in G. Let V be a vector space of dimension n over a field F of characteristic different from 2. Let B be a non-degenerate symmetric,…

A complete classification of finitely generated involutive commutative two-valued groups is obtained. Three series of such two-valued groups are constructed: principal, unipotent and special, and it is shown that any finitely generated…

We classify all finite-dimensional connected Hopf algebras with large abelian primitive spaces. We show that they are Hopf algebra extensions of restricted enveloping algebras of certain restricted Lie algebras. For any abelian matched pair…

A Hom-group G is a nonassociative version of a group where associativity, invertibility, and unitality are twisted by a map \alpha: G\longrightarrow G. Introducing the Hom-group algebra KG, we observe that Hom-groups are providing examples…

We use Fox calculus to assign a marked polytope to a `nice' group presentation with two generators and one relator. Relating the marked vertices to Novikov-Sikorav homology we show that they determine the Bieri-Neumann-Strebel invariant of…

Suppose that $G$ is a group, $H$ and $K$ are proper isomorphic central subgroups of $G$, and $\mathfrak{G}$ is an HNN-extension of $G$ with the associated subgroups $H$ and $K$. We prove necessary and sufficient conditions for…

For each left-invariant Riemannian metric on simply connected nonunimodular Lie groups of dimension four, we determine the full group of isometries.

Hilbert--Lie groups are Lie groups whose Lie algebra is a real Hilbert space whose scalar product is invariant under the adjoint action. These infinite-dimensional Lie groups are the closest relatives to compact Lie groups. Here we study…

A group $\Gamma$ has separable cohomology if the profinite completion map $\iota \colon \Gamma \to \widehat{\Gamma}$ induces an isomorphism on cohomology with finite coefficient modules. In this article, cohomological separability is…

This paper investigates the homology of the Brauer algebras, interpreted as appropriate Tor-groups, and shows that it is closely related to the homology of the symmetric group. Our main results show that when the defining parameter of the…

Let $G=< x,t\mid w>$ be a one-relator group, where $w$ is a word in $x,t$. If $w$ is a product of conjugates of $x$ then, associated with $w$, there is a polynomial $A_w(X)$ over the integers, which in the case when $G$ is a knot group, is…

A binary relation on a finite set is called a Hall relation if it contains a permutation of the set. Under the usual relational product, Hall relations form a semigroup which is known to be a block-group, that is, a semigroup with at most…

A linear group is called unisingular if every element of it has eigenvalue 1. A certain aspect of the theory of abelian varieties requires the knowledge of unisingular irreducible subgroups of the symplectic groups over the field of two…

A relative one-relator presentation has the form P = < X,H ; R > where X is a set, H is a group, and R is a group word on X and H. We show that if the group word on X obtained from R by deleting all the terms from H has what we call the…

Classically, an abelian group $G$ is said to be slender if every homomorphism from the countable product $\mathbb Z^{\mathbb N}$ to $G$ factors through the projection to some finite product $\mathbb Z^n$. Various authors have proposed…

A group obtained from a nontrivial group by adding one generator and one relator which is a proper power of a word in which the exponent-sum of the additional generator is one contains the free square of the initial group and almost always…

In this article, the standard correspondence between the ideal class group of a quadratic number field and the equivalence classes of binary quadratic forms of given discriminant is generalized to any base number field of narrow class…

The main purpose of this paper is to describe some published results and outline corresponding approaches which when applied to automorphism groups of algebras or groups establish that these groups are linear or non-linear.

A Hom-group is the non-associative generalization of a group, whose associativity and unitality are twisted by a compatible bijective map. In this paper, we give some new examples of Hom-groups, and show the first and the second isomorphism…

Let $G$ be a finite group and $H$ a subgroup of $G$. Each left transversal (with identity) of $H$ in $G$ has a left loop (left quasigroup with identity) structure induced by the binary operation of $G$. We say two left transversals are…