Grant Number (asc)
Author Ishikawa, Kazuhiro| Tanaka, Hiroshi| Tanaka, Katsumi| 2002-01 Mathematical Journal of Okayama University volume44 issue1 Journal Article
JaLCDOI 10.18926/11865 Some topologies on stable groups Tanaka, Katsumi| In the theory of Linear algebraic groups, Zariski topology plays a crucial role. We introduce some topologies on general abstract groups generalizing Zariski topology in some sense. Especially we focus on stable groups, because not only the similarity of them with respect to some structure theorems but also we are interested in stable groups for their own right. In Linear algebraic groups, they have a descending chain condition on closed sebsets. Hence we may introduce some topologies on stable groups in order to satisfy the descending chain conditions on closed subsets whatever the topology is. According to this guide line we introduce some topologies stable groups and omega-stable groups. stable groups Z-groups descending chain conditions 岡山大学医療技術短期大学部紀要 1994-01-31 volume4 27 29 0917-4494 日本語 publisher
JaLCDOI 10.18926/15277 Model theory of doubly transitive groups Tanaka, Katsumi| 2重可移群には,near-domainを解釈することができ(定理13), またnear-domainから2重可移群を構成することができる｡つまり,2重可移群の研究はnear-domainの研究と同値になる｡ここで,有限のnear-domainがnear-fieldになることは知られているが,無限のnear-domainがnear-fieldになるかどうかは知られていない｡これに関連して,無限の2重可移群についても多くの未解決問題が残されている｡このノートでは,これらの問題にたいするモデル論的なアプローチ(Morley rank有限の場合の構造析,geometricな方法など)をいくつか紹介する｡ It is well known that we can interpret a near-domain in a doubly-transitive group and we can consruct a doubly-transitive group by a near-domain. This shows the equivalence of the study of doubly-transitive groups and that of near-domains. It is known that every finite near-domain is a near-field, however, it is open in infinite case. We investigate several open problems in this subject and some model theoretic approaches (in case of finite Morley rank, geometric) to them. 置換群 (permutation group) ω-安定 (ω-stable group) Morley rank 2重可移群 (doubly transitive group) 岡山大学医療技術短期大学部紀要 1997-09-10 volume8 issue1 1 6 0917-4494 日本語 publisher