We study the quotient of a free product of groups by the normal closure of a word that is contained in a certain type of 2-generator subgroup, and hence can be expressed in the form of a pushout involving a generalized triangle group. Using the theory of generalized triangle groups, we extend the range of conditions under which a number of results for one-relator products of groups, such as the...

We consider some families of one relator groups arising as fundamental 3-dimensional manifolds, and calculate their character varieties in SL(2, C). Then we give simple geometrical descriptions such varieties, determine the number irreducible components. Our paper relates to work Baker-Petersen, Qazaqzeh Morales-Marcén on variety certain classes groups, but use different methods based concept p...

A program derivation is said to be polytypic if some of its parameters are data types. Polytypic program derivations necessitate a general, non-inductive deenition of`data type'. Here we propose such a dee-nition: a data type is a relator that has membership. It is shown how this deenition implies various other properties that are shared by all data types. In particular, all data types have a u...

If K = Goφ Z where φ is a tame automorphism of the 1-relator group G, then the combinatorial area of loops in a Cayley graph of G is undistorted in a Cayley graph of K. Examples of distortion of area in fibres of fibrations over the circle are given and a notion of exponent of area distortion is introduced and studied. The inclusion of a finitely generated abelian subgroup in the fundamental gr...

A criterion for the HN N-extension of a finite p-group to be residually a finite p-group is obtained and based on this criterion the sufficient condition for residuality a finite p-group of HN N-extension with arbitrary base group is proved. Then these results are applied to give for groups from two classes of one-relator groups the necessary and sufficient condition to be residually a finite p...