Algorithmic problems related to the direct product of groups.
Algorithmic verification of quasi-isometry of some HNN-extensions of Abelian groups.
Algorithmische Probleme bei Einrelatorgruppen und ihre Komplexität.
Algorithms for permutability in finite groups
In this paper we describe some algorithms to identify permutable and Sylow-permutable subgroups of finite groups, Dedekind and Iwasawa finite groups, and finite T-groups (groups in which normality is transitive), PT-groups (groups in which permutability is transitive), and PST-groups (groups in which Sylow permutability is transitive). These algorithms have been implemented in a package for the computer algebra system GAP.
Algunas observaciones acerca de matrices triangulares sobre anillos
All CAT(0) boundaries of a group of the form H × K are CE equivalent
M. Bestvina has shown that for any given torsion-free CAT(0) group G, all of its boundaries are shape equivalent. He then posed the question of whether they satisfy the stronger condition of being cell-like equivalent. In this article we prove that the answer is "Yes" in the situation where the group in question splits as a direct product with infinite factors. We accomplish this by proving an interesting theorem in shape theory.
All completely regular elements in
In Universal Algebra, identities are used to classify algebras into collections, called varieties and hyperidentities are use to classify varieties into collections, called hypervarities. The concept of a hypersubstitution is a tool to study hyperidentities and hypervarieties. Generalized hypersubstitutions and strong identities generalize the concepts of a hypersubstitution and of a hyperidentity, respectively. The set of all generalized hypersubstitutions forms a monoid. In...
All geometries of the Mathieu group based on maximal subgroups.
All subvarieties of a certain variety of semigroups.
All subvarieties of have finite bases of identities.
All Two-Gnerator Fuchsian Group.
All varieties of bands.
All varieties of orthogroups.
Almost all one-relator groups with at least three generators are residually finite
We prove that with probability tending to 1, a one-relator group with at least three generators and the relator of length is residually finite, is a virtually residually (finite -)group for all sufficiently large , and is coherent. The proof uses both combinatorial group theory and non-trivial results about Brownian motions.
Almost associative operations generating a minimal clone
Characterizations of 'almost associative' binary operations generating a minimal clone are given for two interpretations of the term 'almost associative'. One of them uses the associative spectrum, the other one uses the index of nonassociativity to measure how far an operation is from being associative.
Almost Butler groups
Generalizing the notion of the almost free group we introduce almost Butler groups. An almost -group of singular cardinality is a -group. Since almost -groups have preseparative chains, the same result in regular cardinality holds under the additional hypothesis that is a -group. Some other results characterizing -groups within the classes of almost -groups and almost -groups are obtained. A theorem of stating that a group of weakly compact cardinality having a -filtration consisting...
Almost completely decomposable groups with primary cyclic regulating quotient
Almost coproducts of finite cyclic groups
A new class of -primary abelian groups that are Hausdorff in the -adic topology and that generalize direct sums of cyclic groups are studied. We call this new class of groups almost coproducts of cyclic groups. These groups are defined in terms of a modified axiom 3 system, and it is observed that such groups appear naturally. For example, is almost a coproduct of finite cyclic groups whenever is a Hausdorff -primary group and is the group of normalized units of the modular group algebra...
Almost finitely presented soluble groups.
Almost finite-valued -groups