Showing papers on "Free product published in 1988"

Existentially Closed Groups

Abstract: Notation and conventions Introduction Centralizers and normalizers of subgroups -homogeneous groups Recursion theory Applications of the Subgroup theorem The Relative-Subgroup theorem Games Free products First-order of existentially closed groups Bibliography Index.

One-relator quotients and free products of cyclics

Abstract: It is proven that the Freiheitssatz holds for all one-relator products of cyclic groups if the relator is cyclically reduced and a proper power. The method of proof involves representing such groups in PSL2(C) and is a refinement of a technique of Baumslag, Morgan and Shalen. The technique allows the extension of the Freiheitssatz result to many additional one-relator products.

Certain Finitely Generated Compact Zero Dimensional Semigroups

Abstract: Consider a compact zero dimensional (profinite) monoid. While the group of units must be open, a regular D-class need not be open in the ideal it generates. This is the case if and only if the semigroup contains infinitely many copies of a certain semilattice composed of an increasing sequence of idempotents converging to an upper bound.Using compactifications of free products, two generator compact monoids with these properties are constructed.

A converse to a residual finiteness theorem of g. baumslag

Abstract: It is shown that if at least two of the factor groups of a nontrivial amalgamated free product G satisfy nontrivial identities, then a special form of the profinite closure of the associated subgroups is necessary (as well as sufficient) for the residual finiteness of G. An example shows that the necessity no longer holds if only one of the factor groups satisfies an identity.

Sets of disjoint elements in free products of lattice-ordered groups

Abstract: We show that for every infinite cardinal number m there exist two totally ordered abelian groups whose free product in any nontrivial variety of lattice-ordered groups has a disjoint set of cardinality m. This answers problem 10.7 of [13] and extends the results in [12]. We further prove that for the variety of abelian lattice-ordered groups or the variety of all lattice-ordered groups, the free product of two nontrivial members of the variety will always contain an infinite disjoint set.

Free products and the word problem

Abstract: An example is given to show that even in a variety whose free word problem (identity problem) is solvable, the free product of two recursive presentations with solvable word problems may have unsolvable word problem. Under some extra conditions on the syntax of the identities defining the variety however, the free product is shown to preserve solvability of the word problem for recursive presentations. The conditions can be checked mechanically, and common varieties such as semigroups and groups satisfy them, as well as many less familiar varieties. The results are obtained by using rewrite-completion techniques.

Sequential conditions and free products of topological groups

Abstract: If A and B are nontrivial topological groups, not both discrete, such that their free product A џ B is a sequential space, then it is sequential of order ω.

Conjugacy Separability of Some Factor Groups of a Free Product

Abstract: Groups of the form are studied, where is the free product of groups , , and is the th term of the derived series of the Cartesian subgroup of this product. It is proved that if every is conjugacy separable, residually finite with respect to occurrence in cyclic subgroups, and torsion-free, then the groups are conjugacy separable.Bibliography: 8 titles.