\(\Sigma\)-isotype subgroups of local \(k\)-groups (Q2738754)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: \(\Sigma\)-isotype subgroups of local \(k\)-groups |
scientific article; zbMATH DE number 1639878
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(\Sigma\)-isotype subgroups of local \(k\)-groups |
scientific article; zbMATH DE number 1639878 |
Statements
18 December 2001
0 references
mixed Abelian groups
0 references
Warfield groups
0 references
isotype subgroups
0 references
knice subgroups
0 references
primitive elements
0 references
type vectors
0 references
weakly transitive subgroups
0 references
height sequences
0 references
automorphisms
0 references
0.8979301
0 references
0.89046335
0 references
0.8786009
0 references
0.8756059
0 references
0 references
\(\Sigma\)-isotype subgroups of local \(k\)-groups (English)
0 references
Each element of a \(k\)-group is associated with a finite sequence of height sequences called its type vector and automorphisms of the group preserve type vectors. Conversely, a local group is called weakly transitive if whenever two elements have the same height sequence and equal type vectors, then there is an automorphism of the group mapping one of these elements onto the other. One of the major aims of this deep paper is to prove that \(\Sigma\)-isotype subgroups of Warfield groups are weakly transitive. There are a host of applications to local mixed Abelian groups of various types.NEWLINENEWLINEFor the entire collection see [Zbl 0960.00043].
0 references
