Treffer: On the commutator and the center of finite groups: On the commutator and the center of finite groups.
Title:
On the commutator and the center of finite groups: On the commutator and the center of finite groups.
Authors:
Source:
Journal of Algebra. 278:494-501
Publisher Information:
Elsevier BV, 2004.
Publication Year:
2004
Subject Terms:
metanilpotent groups, numerical estimates, derived subgroups, Algebra and Number Theory, Special subgroups (Frattini, Fitting, etc.), Fitting subgroup, Frattini subgroup, Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks, 0101 mathematics, centers, 01 natural sciences, Arithmetic and combinatorial problems involving abstract finite groups, solvable groups
Document Type:
Fachzeitschrift
Article
File Description:
application/xml
Language:
English
ISSN:
0021-8693
DOI:
10.1016/j.jalgebra.2004.03.021
Access URL:
Rights:
Elsevier Non-Commercial
Accession Number:
edsair.doi.dedup.....362049584f861ad4ef2849c0e3c3513c
Database:
OpenAIRE
Weitere Informationen
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.