Author Ishikawa, Kazuhiro| Tanaka, Hiroshi| Tanaka, Katsumi|
Published Date 2002-01
Publication Title Mathematical Journal of Okayama University
Volume volume44
Issue issue1
Content Type Journal Article
JaLCDOI 10.18926/15277
Title Alternative Model theory of doubly transitive groups
FullText URL 008_1_001_006.pdf
Author Tanaka, Katsumi|
Abstract 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。
Abstract Alternative 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.
Keywords 置換群 (permutation group) ω-安定 (ω-stable group) Morley rank 2重可移群 (doubly transitive group)
Publication Title 岡山大学医療技術短期大学部紀要
Published Date 1997-09-10
Volume volume8
Issue issue1
Start Page 1
End Page 6
ISSN 0917-4494
language 日本語
File Version publisher
NAID 120002307870
JaLCDOI 10.18926/11865
Title Alternative Some topologies on stable groups
FullText URL 004_027_029.pdf
Author Tanaka, Katsumi|
Abstract 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.
Keywords stable groups Z-groups descending chain conditions
Publication Title 岡山大学医療技術短期大学部紀要
Published Date 1994-01-31
Volume volume4
Start Page 27
End Page 29
ISSN 0917-4494
language 日本語
File Version publisher
NAID 120002313996