Suppose $G$ is a finite group, $A$ and $B$ are conjugacy classes of $G$ and $eta(AB)$ denotes the number of conjugacy classes contained in $AB$. The set of all $eta(AB)$ such that $A, B$ run over conjugacy classes of $G$ is denoted by $eta(G)$.The aim of this paper is to compute $eta(G)$, $G in { D_{2n}, T_{4n}, U_{6n}, V_{8n}, SD_{8n}}$ or $G$ is a decomposable group of order $2pq$, a group of...

We consider finite colourings of products $$X_1\times X_2\times \cdot \times X_n$$ infinite sets and determine what is the minimal number colours a subproduct $$Y_1\times Y_2\times Y_n$$ subsets could achieve.

suppose $g$ is a finite group, $a$ and $b$ are conjugacy classes of $g$ and $eta(ab)$ denotes the number of conjugacy classes contained in $ab$. the set of all $eta(ab)$ such that $a, b$ run over conjugacy classes of $g$ is denoted by $eta(g)$.the aim of this paper is to compute $eta(g)$, $g in { d_{2n}, t_{4n}, u_{6n}, v_{8n}, sd_{8n}}$ or $g$ is a decomposable group of order $2pq$, a group of...

We investigate a generalization of the Loś-Tarski preservation theorem via the semantic notion of preservation under substructures modulo k-sized cores. It was shown earlier that over arbitrary structures, this semanticnotion for first-order logic corresponds to definability by ∃∀ sentences. In this paper, we identify two properties of classes of finite structures that ensure the above corr...

The goal of this research work was to assist consumers in considering environmental aspects of food consumption. A simplified, modular LCA approach has been used to evaluate the impacts from the consumers' point of view. Comparative LCA's have been calculated for five single aspects of decisions: type of agricultural practice, origin, packaging material, type of preservation, and consumption. T...