Butler Group Direct Decomposition Classification With Applications to Parallel Algorithms

Abstract

The graphical approach to the classification problem of Butler group direct decompositions is used to preserve the indecomposability property of some rigid subgroups in all possible direct decompositions of the group itself. The group class under consideration as well as torsion-free abelian groups as a whole admits non-isomorphic direct decompositions. The proof of decomposition existence with predicted properties is one of the investigation streams. Until now the related results concerned only the ranks of indecomposable summands. Now the way of controlling the other properties of group decompositions is suggested. All the results in this direction are closely connected with the algorithm parallelization. The special feature of the results presented is that they give the method of constructing certain dependence graphs as the subgraphs of the algorithm graph to be given in a parallel form preserving the corresponding fragments. Such dependence subgraphs can define the data relations in parallel computations, which reflect various conditions of parallelism.