The degree pattern of a finite group G was introduced in [15] and denoted by D (G). A finite group M is said to be OD-characterizable if G ≅ M for every finite group G such that |G|=|M| and D (G)= D (M). In this article, we show that the linear groups Lp(2) and Lp+1(2) are OD-characterizable, where 2p-1 is a Mersenne prime. For example, the linear groups L2(2) ≅ S3, L3(2) ≅ L2(7), L4(2) ≅ A8, L5(2), L6(2), L7(2), L8(2), L13(2), L14(2), L17(2), L18(2), L19(2), L20(2), L31(2), L32(2), L61(2), L62(2), L89(2), L90(2), etc., are OD-characterizable. We also show that the simple groups L4(5), L4(7) and U4(7) are OD-characterizable.

Communicated by D. PassmanWe consider the non-commuting graph ∇(G) of a non-abelian finite group G; its vertex set is G\Z(G), the set of non-central elements of G, and two distinct vertices x and y are joined by an edge if [x, y] = 1. We determine the structure of any finite non-abelian group G (up to isomorphism) for which ∇(G) is a complete multipartite graph (see Propositions 3 and 4). It is also shown that a non-commuting graph is a strongly regular graph if and only if it is a complete multipartite graph. Finally, it is proved that there is no non-abelian group whose non-commuting graph is self-complementary and n-cube.

Objective:Polycystic ovary syndrome (PCOS) is the most common endocrine disorder among women of reproductive age. PCOS is considered to be not only a reproductive endocrinopathy, but also a metabolic disorder. The objective of the present study was to characterize the anthropometric and dietary profile of women with PCOS and to compare it with that of healthy age-matched women.Design:In this case-control study, 65 women with PCOS served as cases. The control group consisted of 65 age-matched healthy women. For each participant, demographic, anthropometric and dietary intake data were gathered and compared between the two groups.Results:There was no significant difference between the mean of the body mass index of the two groups, but the mean of waist circumference was significantly higher in the PCOS group, than the control group (P = 0.016). Compared to the normal weight PCOS patients, a significantly higher percentage of overweight patients had hirsutism (P = 0.009). In dietary analysis, women with PCOS consumed more calories and more fat than healthy women (P = 0.001 and P = 0.019, respectively).Conclusion:It is concluded that in PCOS patients, android obesity is a common feature and this abdominal adiposity may be related to the syndrome's complications. PCOS symptoms were more severe in overweight patients than the normal weight. Regarding the dietary pattern, it was indicated that patients with PCOS consume more calories and more fat in their diets and this might have been correlated to their disease.