A remark on a theorem of Baer (Q582390)
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: A remark on a theorem of Baer |
scientific article; zbMATH DE number 4130654
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A remark on a theorem of Baer |
scientific article; zbMATH DE number 4130654 |
Statements
A remark on a theorem of Baer (English)
0 references
1990
0 references
The author proves the following: If G is a group and \(\Sigma\) a set of subgroups of G such that (1) \(G=<\Sigma >\) and \(\Sigma =\Sigma^ G\), (2) if \(A,B\in \Sigma\) then \(<A,B>\) is nilpotent, (3) the \(\Sigma\)-subgroups of G satisfy the maximum condition, then G is nilpotent. This generalizes a theorem of \textit{R. Baer} [Math. Ann. 133, 256-270 (1957; Zbl 0078.015)] which explains the title.
0 references
set of subgroups
0 references
nilpotent
0 references
maximum condition
0 references
