Result: Two-generator subgroups of soluble groups and their Fitting subgroups: Two-generator subgroups of soluble groups and their Fitting subgroups.
Title:
Two-generator subgroups of soluble groups and their Fitting subgroups: Two-generator subgroups of soluble groups and their Fitting subgroups.
Authors:
Source:
Archiv der Mathematik. 80:449-457
Publisher Information:
Springer Science and Business Media LLC, 2003.
Publication Year:
2003
Subject Terms:
finite soluble groups, Special subgroups (Frattini, Fitting, etc.), Fitting subgroups, \(p\)-lengths, two-generator subgroups, Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks, Fitting lengths, 0101 mathematics, 01 natural sciences, Arithmetic and combinatorial problems involving abstract finite groups
Document Type:
Academic journal
Article
File Description:
application/xml
ISSN:
1420-8938
0003-889X
0003-889X
DOI:
10.1007/s00013-003-0765-5
Access URL:
Rights:
Springer TDM
Accession Number:
edsair.doi.dedup.....11288a7e749b23e8af9c33b478842c5c
Database:
OpenAIRE
Further Information
The finite soluble group \(G\) is called an \((F_n)\)-group, if \(G\) satisfies: \((F_n)\): For every \(x,y\in G\), we have \(| F(\langle x,y\rangle)|\leq n\). (Here, \(F(H)\) denotes the Fitting subgroup of the group \(H\).) Let \(p\) be a prime. It is shown that an \((F_n)\)-group is of \(p\)-length one, if \(p^p>n\) for a Fermat prime \(p\) or \(p^{p+1}>n\) otherwise. Moreover, the Fitting length of \((F_n)\)-groups is bounded by a function of \(n\) given explicitly.