In this paper, the non-abelian simple groups having at most 20 distinct irreducible character degrees are classified.

Introduction: Health care industry also patients penalized by medical errors that are inevitable but highly preventable. Vast majority of medical errors are related to adverse drug reactions, while drug-drug interactions (DDIs) are the main cause of adverse drug reactions (ADRs). DDIs and ADRs have mainly been reported by haphazard case studies. Experimental in vivo and in vitro researches also reveals DDI pairs. Laboratory and experimental researches are valuable but also expensive and in some cases researchers may suffer from limitations. Methods: In the current investigation, the latest published works were studied to analyze the trend and pattern of the DDI modelling and the impacts of machine learning methods. Applications of computerized techniques were also investigated for the prediction and interpretation of DDIs. Results: Computerized data-mining in pharmaceutical sciences and related databases provide new key transformative paradigms that can revolutionize the treatment of diseases and hence medical care. Given that various aspects of drug discovery and pharmacotherapy are closely related to the clinical and molecular/biological information, the scientifically sound databases (e.g., DDIs, ADRs) can be of importance for the success of pharmacotherapy modalities. Conclusion: A better understanding of DDIs not only provides a robust means for designing more effective medicines but also grantees patient safety.

Let cd(G) be the set of all irreducible complex characters of a finite group G. In [4], Lewis proved that if p, q, r, and s are distinct primes and cd(G) = {1, p, q, r, pq, pr} or cd(G) = {1, p, q, r, s, pr, ps, qr, qs}, then G is the direct product of two normal non-abelian subgroups of G. We generalize Lewis' results by loosening the primeness hypothesis of cd(G).

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