Groups of Mixed Type
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Proceedings of the International Conference on Technology in Mathematics Education (Auckland, NZ, December 11-14, 2000)
DOCUMENT RESUME ED 474 050 SE 066 920 AUTHOR Thomas, M.O.J., Ed. TITLE Proceedings of the International Conference on Technology in Mathematics Education (Auckland, NZ, December 11-14, 2000). INSTITUTION Auckland Inst. of Tech.(New Zealand). PUB DATE 2000-12-00 NOTE 295p.; For plenary papers, see SE 066 921-925, SE 066 927. AVAILABLE FROM Aukland University of Technology, PB 92006, Auckland, NZ. Tel: 64-9-907-999 X 8405; Fax: 64-9-307-9973; e-mail: [email protected] or University of Auckland PB 92019, Auckland, NZ. Tel: 64-9-373-7599 X 5886; Fax: 64-9-373-7457; e-mail: [email protected]. PUB TYPE Collected Works Proceedings (021) Reports Descriptive (141) EDRS PRICE EDRS Price MF01/PC12 Plus Postage. DESCRIPTORS *Cognitive Processes; Algebra; Calculators; *Computer Uses in Education; Cultural Influences; *Educational Assessment; Elementary Secondary Education; Geometric Concepts; Geometry; *Graphing Calculators; Graphs; *Mathematics Curriculum; Mathematics Instruction; Problem Solving; Statistics; Teaching Methods; Thinking Skills IDENTIFIERS *Computer Algebra ABSTRACT This volume contains the proceedings of the International Conference on Technology in Mathematics Education (TIME 2000). It includes papers, posters, and short oral reports. Research papers include: (1) "Implications of the Shift from Isolated Expensive Technology to Connected, Inexpensive, Ubiquitous and Diverse Technologies" (Jim Kaput); (2) "Developing Simulation Activities to Improve Students' Statistical Reasoning" (Beth Chance, Joan Garfield, and Robert delMas); (3) "Technology and Versatile Thinking in Mathematics" (David Tall); (4) "A Strategy for the Use of Technology to Enhance Learning and Teaching in Maths, Stats.and OR" (Pam Bishop and Neville Davies);(5) "Technology and the Curriculum: The Case of the Graphics Calculator" (Barry Kissane); (6) "What Mathematical Abilities Are Most Needed for Success Beyond School in a Technology Based Age of Information?" (Richard Lesh); (7) "Mathematics in Action: Two New Zealand Case Studies" (David M. -
Groups of Finite Morley Rank with Strongly Embedded Subgroups
JOURNAL OF ALGEBRA 180, 778]807Ž. 1996 ARTICLE NO. 0093 Groups of Finite Morley Rank with Strongly Embedded Subgroups Tuna Altinel Department of Mathematics, Rutgers Uni¨ersity, New Brunswick, New Jersey 08903 Communicated by Gernot Stroth Received February 5, 1995 1. INTRODUCTION The central problem in the area of groups of finite Morley rank is the Cherlin]Zil'ber conjecture, which states that an infinite simple group of finite Morley rank is an algebraic group over an algebraically closed field. This conjecture can be divided into three parts. Conjecture 1. There exist no nonsolvable connected groups of finite Morley rank all of whose proper definable connected subgroups are nilpotent; such groups are called bad groups. Conjecture 2. There exists no structure ²:K, q, ? , A of finite Morley rank where K is an algebraically closed field and A is an infinite proper definable subgroup of the multiplicative group of K; such structures are called bad fields. Conjecture 3. A simple group of finite Morley rank which does not have definable bad sections and in which no bad fields are interpretable is an algebraic group over an algebraically closed field. In connection with Conjecture 3, one makes the following definition: DEFINITION 1.1. A group of finite Morley rank which does not have definable bad sections and in which no bad fields are interpretable is called a tame group. In order to classify simple tame groups of finite Morley rank a program based on ideas borrowed from finite group theory has been developed by Alexander Borovik. This paper is part of this program. -
E 20 I O'l'f'l9
............. .~,?; -:7~.~! Math. Forsdwngslnstttut 0berw0Ifach. E 20 I o'L'f'l9 MATHEMATISCHES FORSCHUl'iGSINSTITUt' 0 DER\VO LFACH T ag u n g s b er c h t 1/1994 i\1()OELLTHEORIE 02.01. bis 08.01.1994 Die Tagung fand unter der Leitung von U. Felgner (Thübingen),.:\. Prestcl (!{onstallz) und M. Ziegler (Freiburg) statt. In1 Vordergrund standen die T.hemen "Modelltheorie 'Yon Gruppen·~. speziell die 'sluall index property' für Strukturen, sowie Hrushovski's Beweis der ~\'lordell-Lang VernllltUng im Funktionenk~rperfalL Zu heiden Sch\verpunkten fanden nlehrere Hauptvort.räge statt. Darüberhinaus \vurden in Kurzvorträgen Ergebnisse aus der Stabilit~theorieund aus der . i\1o~elltheorie spezieller Strukturen'(Gruppen, Moduln, o-miJii~ale Strukturen. Graphen) vorgestellt. Vortragsausziige The field Qlr of totally real algebraic ·numbers is decidable Dan HaraIl, Tel Avjv (.~ joint. work with !vl. Fricd and H. Viilklt:ill., Thc rcsült in thc titlc reHes on two facts: Theorem A (Pop): Qlr is pseuclo real dOSt'cl (rRC). © Theorenl B: Thc absolut Galois group G(Qtr) of Qtr is the fn~e protinitc procltu:t b of " copics ur 7l/2Z over thc Calltof spa.cc. Eqllivalt"!utly (as Qtr is COlllltahlc) G = G(Qtr) has the following EIUbedc.lillg property (EP); i) G is generated by luv(G), thc set of involutious in G; ii) Given an epituorphislIl of finite groups 0': B --+ A, a contillllOllS Cpilllo"rphisin cp: G -+ A, and asubset Ia ~ Illv(B) closed under thc coujugation in B ,uld such that B = (lu) and treIB) = <p(Illv(G», there is a continuons epimorphislll t/J: G -+' B such that OlOVJ = <p and t/J(Inv(G» = IB. -
PDF of Program of the Sessions
Program of the Sessions Denver, Colorado, January 15–18, 2020 Monday, January 13 AMS Short Course Reception AMS Short Course on Mean Field Games: 5:00 PM –6:00PM Capitol Ballroom 1,2,3, Agent Based Models to Nash Equilibria 4th Floor, Hyatt Regency Denver 9:00 AM –6:00PM Capitol Ballroom 1,2,3, 4th Floor, Hyatt Regency Denver Organizer: Franc¸ois Delarue, University of Nice 9:00AM Registration Tuesday, January 14 9:45AM Introduction AWM Moving Towards Action Workshop 10:00AM The Nash certainty equivalence and 8:00 AM –5:00PM Denver 1,2, Hilton (1) applications. Denver City Center Roland P. Malham´e, Polytechnique Montr´eal Organizers: Maeve McCarthy, Murray 11:30AM Break State University Elizabeth Donovan, Murray 11:30AM The Nash certainty equivalence and State University (2) applications: Exercise Session. Christy V. Graves, Princeton University Vrushali Bokil,Oregon State University NOON Lunch Ami Radunskaya, Pomona 2:00PM The Master Equation. College (3) F. Delarue, Universite Cote d’Azur, Moderator: Karoline Pershell, France Association for Women in 3:15PM Discussion and Break Mathematics 4:00PM Applications of Mean Field Games in AMS Department Chairs Workshop (4) Economic Theory. Rene Carmona, Princeton University, 8:00 AM –6:30PM Capitol Ballroom 4, 4th 5:00PM Reception Floor, Hyatt Regency Denver The time limit for each AMS contributed paper in the sessions meeting will be found in Volume 41, Issue 1 of Abstracts is ten minutes. The time limit for each MAA contributed of papers presented to the American Mathematical Society, paper varies. In the Special Sessions the time limit varies ordered according to the numbers in parentheses following from session to session and within sessions. -
Tame and Wild Finite Subgroups of the Plane Cremona Group
TAME AND WILD FINITE SUBGROUPS OF THE PLANE CREMONA GROUP IGOR V. DOLGACHEV To the memory of Vasily Iskovskikh Abstract. We survey some old and new results about finite subgroups of the Cremona group Crn(k) of birational automorphisms of the pro- jective n-space over a field k. Contents 1. Introduction 1 2. General facts 2 2.1. G-varieties 2 2.2. Lift to characteristic 0 3 3. The case k = C 4 3.1. Conic bundles 4 3.2. De Jonqui`erestransformations 6 3.3. Automorphism groups of Del Pezzo surfaces 8 3.4. Elementary links 23 3.5. Final classification 25 4. Cyclic tame subgroups of Cr2(k), where k is a perfect field 29 4.1. Elements of finite order in reductive algebraic groups 29 4.2. Elements of order ≥ 7 30 5. Wild cyclic groups 32 5.1. Conic bundles 32 5.2. Del Pezzo surfaces 33 6. Wild simple groups 36 6.1. Projective linear groups 36 6.2. Conic bundles 38 6.3. Del Pezzo surfaces 39 References 43 1. Introduction The Cremona group Crn(k) of degree n over a field k is the group of n birational automorphisms of Pk . In algebraic terms Crn(k) = Autk(k(t1, . , tn)). 1 2 IGOR V. DOLGACHEV In this article I will survey some old and new results on classification of of conjugacy classes of finite subgroups of Cr2(k). Recall that in the case n = 1, we have ∼ 1 ∼ Cr1(k) = Aut(Pk) = PGL2(k). The classification of finite subgroups of PGL2(k) is well-known.