For a finite group G, the representation dimension is the smallest integer realizable as the degree of a complex faithful representation of G. In this article, we compute representation dimension for some p-groups, their direct products, and groups with certain conditions on nonlinear irreducible characters. We also make similar computations for the smallest integer realizable as the degree of an irreducible complex faithful representation of G, if one exists. In the appendix, we present GAP codes to compute these numbers.

Background Obesity is characterized by the abnormal or excessive deposition of fat in the adipose tissues. The recent rise in incidence of obesity in both developed as well as developing nations are a matter of grave concern due to the well-established association between obesity and several other chronic conditions.Aim The objective of the present study was to verify the potential association between obesity and periodontal disease among Indians.Methodology Using random sampling 200 subjects aged 20 to 60 years from the state of Punjab were evaluated at a given time using the Community Periodontal Index CPI and periodontitis was defined as ge ldquocode 3.rdquo Body mass index BMI and waist circumference WC were used to represent the measures of overall body fat and upper body fat respectively. BMI and WC cutoff points used in the present study are as established by the World Health Organization.Results There was a positive correlation between BMI and periodontitis in both males and females while WC was highly significantly associated with periodontitis only in females.Conclusion Within the limitations of this study it can be concluded that obese individuals are at a higher risk for developing periodontitis.