Finite groups and geometries: a view on the present state and on the future

The model: groups of Lie-Chevalley type and buildingsThis paper is not the presentation of a completed theory but rather a report on a search progressing as in the natural sciences in order to better understand the relationship between groups and incidence geometry, in some future sought-after theory Τ. The search is based on assumptions and on wishes some of which are time-dependent, variations being forced, in particular, by the search itself.A major historical reference for this subject is, needless to say, Klein's Erlangen Programme. Klein's views were raised to a powerful theory thanks to the geometric interpretation of the simple Lie groups due to Tits (see for instance), particularly his theory of buildings and of groups with a BN-pair (or Tits systems). Let us briefly recall some striking features of this.Let G be a group of Lie-Chevalley type of rank r, denned over GF(q), q = pn, p prime. Let Xr denote the Dynkin diagram of G. To these data corresponds a unique thick building B(G) of rank r over the Coxeter diagram Xr (assuming we forget arrows provided by the Dynkin diagram). It turns out that B(G) can be constructed in a uniform way for all G, from a fixed p-Sylow subgroup U of G, its normalizer NG(U) and the r maximal subgroups of G containing NG(U).

Adjuvant chemotherapy in elderly patients with breast cancer: a survey of the Breast International Group (BIG).

BACKGROUND: To collect oncologists' experience and opinion on adjuvant chemotherapy in elderly breast cancer patients. MATERIALS AND METHODS: A questionnaire was circulated among the members of the Breast International Group. RESULTS: A total of 277 oncologists from 28 countries participated in the survey. Seventy years is the age cut-off commonly used to define a patient as elderly. Biological age and the biological characteristics of the tumor are the most frequently used criteria to propose adjuvant chemotherapy to an elderly patient. Combination therapy with cyclophosphamide, methotrexate and fluorouracil on days 1 and 8 is the most frequently prescribed regimen. Great interest exists in oral chemotherapy. CONCLUSION: There is interest among those who responded to the survey to validate a comprehensive geriatric assessment for use as a predictive instrument of toxicity and/or activity of anticancer therapy and to evaluate the role of a treatment option that is potentially less toxic and possibly as effective as polychemotherapy.