Publicado
A self-contained guide to Frécon's theorem
Una guía autocontenida al teorema de Frécon
DOI:
https://doi.org/10.15446/recolma.v55n2.102739Palabras clave:
groups of finite Morley rank, bad groups (en)Grupos de rango de Morley finito, grupos malos (es)
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A streamlined exposition of Frécon's theorem on non-existence of bad groups of Morley rank 3. Systematising ideas by Poizat and Wagner, we avoid incidence geometries and use group actions instead; the proof becomes short and completely elementary.
Presentamos una breve demostración depurada del teorema de Frécon sobre la no existencia de grupos malos de rango de Morley 3. Abstrayendo ideas de Poizat y Wagner, evitamos el uso de las geometrías de incidencia. En su lugar usamos acciones de grupos; así la demostración se torna verdaderamente elemental y concisa.
Referencias
A. Borovik and A. Nesin, Groups of finite Morley rank, Oxford Logic Guides, vol. 26, The Clarendon Press, Oxford University Press, New York, 1994, Oxford Science Publications. MR MR1321141 (96c:20004)
G. Cherlin, Groups of small Morley rank, Ann. Math. Logic 17 (1979), no. 1-2, 1-28. MR 552414 (81h:03072)
A. Deloro and J. Wiscons, The geometry of involutions in ranked groups with a TI-subgroup, JLMS 52 (2020), no. 3, 411-428.
O. Frécon, Simple groups of Morley rank 3 are algebraic, J. Amer. Math. Soc. 31 (2018), no. 3, 643-659. MR 3787404
B. Poizat, Milieu et symétrie, une étude de la convexité dans les groupes sans involutions, J. Algebra 497 (2018), 143-163. MR 3743178
B. Poizat and F. Wagner, Comments on a theorem by Olivier Frécon, Preprint arXiv:1609.06229 (Modnet 1095), 2016.
J. Reineke, Minimale Gruppen, Z. Math. Logik Grundlagen Math. 21 (1975), no. 4, 357-359. MR 0379179 (52 #85)
F. Wagner, Bad groups, Mathematical Logic and its Applications (Makoto Kikuchi, ed.), RIMS Kôkyûroku, vol. 2050, Kyoto University, Kyoto, 2017, pp. 57-66.
