Some aspects of simplicity in the analysis of block designs

In this article, we develop and examine a group-theoretic approach to the notion of simplicity in the analysis of block designs. This calls for invariance considerations (in a specialized sense). The defining conditions (for simplicity) in this approach, as they stand, appear to be quite rigid. We have, therefore, imposed some weaker conditions and examined further aspects of the problem. The results seem to be quite interesting.