On the commutator and the center of finite groups. (Q1882982)
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: On the commutator and the center of finite groups. |
scientific article; zbMATH DE number 2105340
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the commutator and the center of finite groups. |
scientific article; zbMATH DE number 2105340 |
Statements
On the commutator and the center of finite groups. (English)
0 references
1 October 2004
0 references
The authors give numerical bounds for solvable groups, connecting the orders of \(G\) and \(G'\). Example: If \(|G'|^3\leq|G|\neq 1\), then \(\Phi(G)\neq 1\) or \(Z(G)\neq 1\) (Corollary A1). The result is strengthened if the minimal and maximal prime dividing the order is given. Consequences for metanilpotent groups and groups with nilpotent commutator subgroup are given.
0 references
numerical estimates
0 references
centers
0 references
derived subgroups
0 references
Fitting subgroup
0 references
Frattini subgroup
0 references
solvable groups
0 references
metanilpotent groups
0 references
