Using the Simplex Code to Construct Relative Difference Sets in 2-groups

Relative Difference Sets with the parameters (2a, 2b, 2a, 2a-b) have been constructed many ways (see [2], [3], [5], [6], and [7] for examples). This paper modifies an example found in [1] to construct a family of relative difference sets in 2-groups that gives examples for b = 2 and b = 3 that have a lower rank than previous examples. The Simplex code is used in the construction

New Constructions of Menon Difference Sets

Menon difference sets have parameters (4N2, 2N2 − N, N2 − N). These have been constructed for N = 2a3b, 0 ⩽ a,b, but the only known constructions in abelian groups require that the Sylow 3-subgroup be elementary abelian (there are some nonabelian examples). This paper provides a construction of difference sets in higher exponent groups, and this provides new examples of perfect binary arrays

Impact on quality-of-life: before and after topical combinational treatment in patients of acne vulgaris

Background: The objective was to study quality-of-life in patients of acne vulgaris before and after treatment by benzoyl peroxide 2.5% gel and clindamycin 1% gel or benzoyl peroxide 2.5% gel and nadifloxacin 1% cream or tretinoin 0.025% and clindamycin 1% gel.Methods: This was a prospective, open, randomized, parallel comparative study of 60 patients of acne vulgaris attending the Department of Dermatology and Venereal Diseases, Government Medical College, Rajindra Hospital, Patiala. Three groups were made 20 in each group, one group received benzoyl peroxide 2.5% gel and clindamycin 1% gel, the second group received benzoyl peroxide 2.5% gel, and nadifloxacin 1% cream and the third group received tretinoin 0.025% and clindamycin 1% gel. Cardiff acne disability index questionnaire was filled before starting and after the treatment.Results: In these three groups, it was found that the group on benzoyl peroxide 2.5% gel and clindamycin 1% gel, mean score, before starting treatment was 8.35±3.48 and after treatment was 2.95±2.09 (p<0.001), group on benzoyl peroxide 2.5% gel and nadifloxacin 1% cream, mean score, before starting treatment was 7.60±3.75 and after treatment was 5.80±2.98 (p<0.001) and group on tretinoin 0.025% and clindamycin 1% gel mean score is 8.00±3.06 and after treatment was 5.40±2.93 (p<0.001).Conclusion: Quality-of-life improves more in patients taking benzoyl peroxide 2.5% gel and clindamycin 1% gel, and then, tretinoin 0.025% and clindamycin 1% gel and then benzoyl peroxide 2.5% gel and nadifloxacin 1% cream

FΠ Projectors of Π soluble groups

AbstractLet F be any Schunk class and Π any set of primes. Define FΠ as the class of all groups having a normal Π′ complement in G and a Hall Π-subgroup of G belonging to F. If G is any finite Π soluble group, then 1.(a) G has an FΠ projector,2.(b) all FΠ projectors are conjugate. Some very interesting properties of FΠ projectors are shown

Weak Cayley tables

In [1] Brauer puts forward a series of questions on group representation theory in order to point out areas which were not well understood. One of these, which we denote by (B1), is the following: what information in addition to the character table determines a (finite) group? In previous papers [5, 7–13], the original work of Frobenius on group characters has been re-examined and has shed light on some of Brauer's questions, in particular an answer to (B1) has been given as follows. Frobenius defined for each character χ of a group G functions χ(k):G(k) → C for k = 1, …, degχ with χ(1) = χ. These functions are called the k-characters (see [10] or [11] for their definition). The 1-, 2- and 3-characters of the irreducible representations determine a group [7, 8] but the 1- and 2-characters do not [12]. Summaries of this work are given in [11] and [13]