A note on finite groups with few values in a column of the character table

Many structural properties of a finite group G are encoded in the set of irreducible character degrees of G. This is the set of (distinct) values appearing in the "first" column of the character table of G. In the current article, we study groups whose character table has a "non-first" column satisfying one particular condition. Namely, we describe groups having a nonidentity element on which all nonlinear characters take the same value

Prime power indices in factorised groups

[EN] Let the group G = AB be the product of the subgroups A and B. We determine some structural properties of G when the p-elements in A. B have prime power indices in G, for some prime p. More generally, we also consider the case that all prime power order elements in A. B have prime power indices in G. In particular, when G = A = B, we obtain as a consequence some known results.The first author is supported by Proyecto Prometeo II/2015/011, Generalitat Valenciana (Spain), and the second author is supported by Proyecto MTM2014-54707-C3-1-P, Ministerio de Economia, Industria y Competitividad (Spain). The results in this paper are part of the third author's Ph.D. thesis, and he acknowledges the predoctoral grant ACIF/2016/170, Generalitat Valenciana (Spain).Felipe Román, MJ.; Martínez-Pastor, A.; Ortiz-Sotomayor, VM. (2017). Prime power indices in factorised groups. Mediterranean Journal of Mathematics. 14(6):1-15. https://doi.org/10.1007/s00009-017-1023-6S115146Amberg, B., Franciosi, S., de Giovanni, F.: Products of Groups. Oxford University Press Inc., New York (1992)Baer, R.: Group elements of prime power index. Trans. Am. Math. Soc. 75, 20–47 (1953)Ballester-Bolinches, A., Cossey, J., Li, Y.: Mutually permutable products and conjugacy classes. Monatsh. Math. 170, 305–310 (2013)Ballester-Bolinches, A., Esteban-Romero, R., Asaad, M.: Products of finite groups, vol. 53 of de Gruyter Expositions in Mathematics, Berlin (2010)Berkovich, Y., Kazarin, L.S.: Indices of elements and normal structure of finite groups. J. Algebra 283, 564–583 (2005)Camina, A.R., Camina, R.D.: Implications of conjugacy class size. J. Group Theory 1(3), 257–269 (1998)Camina, A.R., Shumyatsky, P., Sica, C.: On elements of prime-power index in finite groups. J. Algebra 323, 522–525 (2010)Chillag, D., Herzog, M.: On the length of the conjugacy classes of finite groups. J. Algebra 131, 110–125 (1990)Doerk, K., Hawkes, T.: Finite Soluble Groups, vol. 4 of de Gruyter Expositions in Mathematics, Berlin (1992)Felipe, M.J., Martínez-Pastor, A., Ortiz-Sotomayor, V.M.: On finite groups with square-free conjugacy class sizes. Int. J. Group Theory (to appear)Kurzweil, H., Stellmacher, B.: The theory of finite groups: an introduction. Springer, New York (2004)Liu, X., Wang, Y., Wei, H.: Notes on the length of conjugacy classes of finite groups. J. Pure Appl. Algebra 196, 111–117 (2005

Polyethylene thickness is a risk factor for wear necessitating insert exchange

PURPOSE: The aim of this observational study was to investigate the optimal minimal polyethylene (PE) thickness in total knee arthroplasty (TKA) and identify other risk factors associated with revision of the insert due to wear. METHODS: A total of 84 TKA were followed for 11-16 years. All patients received the same prosthesis design (Interax; Howmedica/ Stryker) with halfbearings: separate PE-inserts medially and laterally. Statistical analysis comprised Cox-regression to correct for confounding. RESULTS: Eight knees (9.5%) had been revised due to thinning inserts and an additional patient is scheduled for revision. PE thickness, diagnosis, BMI and weight are risk factors for insert exchange. For each millimetre decrease in PE thickness, the risk of insert exchange increases 3.0 times, which remains after correction for age, gender, weight, diagnosis and femoral-tibial angle. Insert exchange was 4.73 times more likely in OA-patients compared to RA-patients. For every unit increase in BMI and weight the risk for insert exchange increases 1.40 times and 1.14 times, respectively. CONCLUSIONS: In conclusion we therefore advise against the use of thin PE inserts in modular TKA and recommend PE inserts with a minimal 8-mm thickness.Optimising joint reconstruction management in arthritis and bone tumour patient

Bone Mineral Density in HIV-Negative Men Participating in a Tenofovir Pre-Exposure Prophylaxis Randomized Clinical Trial in San Francisco

Pre-exposure prophylaxis (PrEP) trials are evaluating regimens containing tenofovir-disoproxil fumarate (TDF) for HIV prevention. We determined the baseline prevalence of low bone mineral density (BMD) and the effect of TDF on BMD in men who have sex with men (MSM) in a PrEP trial in San Francisco.We evaluated 1) the prevalence of low BMD using Dual Energy X-ray Absorptiometry (DEXA) in a baseline cohort of 210 HIV-uninfected MSM who screened for a randomized clinical trial of daily TDF vs. placebo, and 2) the effects of TDF on BMD in a longitudinal cohort of 184 enrolled men. Half began study drug after a 9-month delay to evaluate changes in risk behavior associated with pill-use. At baseline, 20 participants (10%) had low BMD (Z score≤-2.0 at the L2-L4 spine, total hip, or femoral neck). Low BMD was associated with amphetamine (OR = 5.86, 95% CI 1.70-20.20) and inhalant (OR = 4.57, 95% CI 1.32-15.81) use; men taking multivitamins, calcium, or vitamin D were less likely to have low BMD at baseline (OR = 0.26, 95% CI 0.10-0.71). In the longitudinal analysis, there was a 1.1% net decrease in mean BMD in the TDF vs. the pre-treatment/placebo group at the femoral neck (95% CI 0.4-1.9%), 0.8% net decline at the total hip (95% CI 0.3-1.3%), and 0.7% at the L2-L4 spine (95% CI -0.1-1.5%). At 24 months, 13% vs. 6% of participants experienced >5% BMD loss at the femoral neck in the TDF vs. placebo groups (p = 0.13).Ten percent of HIV-negative MSM had low BMD at baseline. TDF use resulted in a small but statistically significant decline in BMD at the total hip and femoral neck. Larger studies with longer follow-up are needed to determine the trajectory of BMD changes and any association with clinical fractures.ClinicalTrials.gov: NCT00131677

Finite groups with many values in a column or a row of the character table

Many results show how restrictions on the degrees of the irreducible characters of a finite group G, influence the structure of G. In the current article we study groups with restrictions on the values of a nonidentity rational element of the group G. We show that the symmetric group on 3 letters is the only nonabelian finite group that contains a rational element g assuming different values on any two distinct irreducible characters. We comment that the dual statement is also true

A note on finite groups with few values in a column of the character table

Many structural properties of a finite group G are encoded in the set of irreducible character degrees of G. This is the set of (distinct) values appearing in the "first" column of the character table of G. In the current article, we study groups whose character table has a "non-first" column satisfying one particular condition. Namely, we describe groups having a nonidentity element on which all nonlinear characters take the same value

Groups with reality and conjugacy conditions

Many results were proved on the structure of finite groups with some restrictions on their real elements and on their conjugacy classes. We generalize a few of these to some classes of infinite groups. We study groups in which real elements are central, groups in which real elements are 2-elements, groups in which all non-trivial classes have the same finite size and FC-groups with two non-trivial conjugacy class sizes

Primitive normal matrices and covering numbers of finite groups

A primitive matrix is a square matrix M with nonnegative real entries such that the entries of M s are all positive for some positive integer s. The smallest such s is called the primitivity index of M. Primitive matrices of normal type (namely: MM T and M T M have the same zero entries) occur naturally in studying the so called ”conjugacy-class covering number ” and ”character covering number” of a finite group. We show that if M is a primitive n n matrix of normal type with minimal polynomial of degree m, then the primitivity index of n M is at most + 1 (m 1). This bound is then applied to improve know