Subgroups of Rank One Groups
β Scribed by Franz Georg Timmesfeld
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 81 KB
- Volume
- 234
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
In this paper we prove the following theorem: THEOREM 1.5. Let G be an infinite, simple, K \*-group of finite Morley rank with a strongly embedded subgroup M. Assume that the Sylow 2-subgroups of G ha¨e infinitely many commuting in¨olutions. Then M is sol¨able. Ž . If, in addition, G is tame, then
A sufficient condition is obtained for the residual torsion-free nilpotence of certain finitely presented metabelian groups that arise from a matrix representa-Ε½ . tion developed by Magnus 1939, Ann. of Math. 40, 764α768 for metabelian Ε½ groups. Using this condition and a construction due to Baumsla
A group is said to have finite special rank F s if all of its finitely generated subgroups can be generated by s elements. Let G be a locally finite group and suppose that HrH has finite rank for all subgroups H of G, where H denotes the normal core of H in G. We prove that then G has an abelian no
Conjecture 1 (Even Type Conjecture). Let G be a simple group of finite Morley rank of even type, with no infinite definable simple section of degenerate type. Then G is algebraic.