Department of Mathematics, Faculty of Science, Okayama University Acta Medica Okayama 0030-1566 44 1 2002 Ladder Index of Groups 37 42 EN Kazuhiro Ishikawa Hiroshi Tanaka Katsumi Tanaka 10.18926/mjou/33123 No potential conflict of interest relevant to this article was reported.

岡山大学医療技術短期大学部 Acta Medica Okayama 0917-4494 8 1 1997 2重可移群のモデル理論 1 6 EN Katsumi Tanaka 10.18926/15277 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｡ No potential conflict of interest relevant to this article was reported.

岡山大学医療技術短期大学部 Acta Medica Okayama 0917-4494 4 1994 安定群の上の位相について 27 29 EN Katsumi Tanaka 10.18926/11865 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. No potential conflict of interest relevant to this article was reported.