A Cayley digraph X = Cay(G, S) is said to be normal for G if the regular representation R(G) of G is normal in the full automorphism group Aut(X ) of X . A characterization of normal minimal Cayley digraphs for abelian groups is given. In addition, the abelian groups, all of whose minimal Cayley dig
Minimal Normal Subgroups of Dinilpotent Groups
โ Scribed by Derek J.S. Robinson; Stewart E. Stonehewer
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 94 KB
- Volume
- 234
- Category
- Article
- ISSN
- 0021-8693
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โฆ Synopsis
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.
๐ SIMILAR VOLUMES
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## 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.