Let A be the collection of groups which can be assembled from infinite cyclic groups using the binary operations free and direct product. These groups can be described in several ways by graphs. The group (Z ∗Z)×(Z ∗Z) has been shown by [1] to have a rich subgroup structure. In this article we examine subgroups of A–groups. DefineA to be the smallest class of groups which contains the infinite ...

in this paper we study a representation of a fuzzy subgroup $mu$ of a group $g$, as a product of indecomposable fuzzy subgroups called the components of $mu$.  this representation is unique up to the number of components and their isomorphic copies. in the crisp group theory, this is a well-known theorem attributed to remak, krull, and schmidt. we consider the lattice of fuzzy subgroups and som...

We investigate the structure of subdirect products of groups, particularly their finiteness properties. We pay special attention to the subdirect products of free groups, surface groups and HNN extensions. We prove that a finitely presented subdirect product of free and surface groups virtually contains a term of the lower central series of the direct product or else fails to intersect one of t...

covering arrays of strength two have been widely studied as combinatorial models of software interaction test suites for pairwise testing. while numerous algorithmic techniques have been developed for the generation of covering arrays with few columns (factors), the construction of covering arrays with many factors and few tests by these techniques is problematic. random generation techniques c...

in this note first by considering the notion of general fuzzy automata (for simplicity gfa), we define the notions of direct product, restricted direct product and join of two gfa. also, we introduce some operations on (fuzzy) sets and then prove some related theorems. finally we construct the general fuzzy recognizers and recognizable sets and give the notion of (trim) reversal of a given gfa....

To better understand groups it is often useful to see how a group can be built from smaller groups. For example, given two groups G and H, we can form the direct product G × H. This new group can be studied in terms of the two pieces from which it is built. However, the direct product construction is too special to understand most groups. In other words, most groups are not expressible as the d...