If a finite group G is the product of two nilpotent subgroups A and B and if N is a minimal normal subgroup of G, then AN or BN is nilpotent. This result is extended to several classes of infinite groups.
ON DEFINABILITY OF NORMAL SUBGROUPS OF A SUPERSTABLE GROUP
โ Scribed by Akito Tsuboi
- Publisher
- John Wiley and Sons
- Year
- 1992
- Tongue
- English
- Weight
- 319 KB
- Volume
- 38
- Category
- Article
- ISSN
- 0044-3050
No coin nor oath required. For personal study only.
โฆ Synopsis
Abstract
In this note we treat maximal and minimal normal subgroups of a superstable group and prove that these groups are definable under certain conditions. Main tool is a superstable version of Zil'ber's indecomposability theorem. MSC: 03C60.
๐ SIMILAR VOLUMES
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