Result: Finite Groups of Bounded Rank with an Almost Regular Automorphism of Prime Order: Finite groups of bounded rank with an almost regular automorphism of prime order
Title:
Finite Groups of Bounded Rank with an Almost Regular Automorphism of Prime Order: Finite groups of bounded rank with an almost regular automorphism of prime order
Authors:
Source:
Siberian Mathematical Journal. 43:955-962
Publisher Information:
Springer Science and Business Media LLC, 2002.
Publication Year:
2002
Subject Terms:
regular automorphisms, 0102 computer and information sciences, 01 natural sciences, Automorphisms of abstract finite groups, G100 - Mathematics, Algebra, nilpotent subgroups, Finite nilpotent groups, \(p\)-groups, Associated Lie structures for groups, nilpotency classes, 0101 mathematics, associated Lie rings, Arithmetic and combinatorial problems involving abstract finite groups, rank of finite groups
Document Type:
Academic journal
Article
File Description:
application/xml
Language:
English
ISSN:
1573-9260
0037-4466
0037-4466
DOI:
10.1023/a:1020171227191
Access URL:
Rights:
Springer Nature TDM
CC BY
CC BY
Accession Number:
edsair.doi.dedup.....82a0c9fecffcd43bc347d6cb5a1eaa4e
Database:
OpenAIRE
Further Information
The main result reads as follows: Let \(G\) be a finite group of rank \(r\), let \(\varphi\) be an automorphism, and let \(|C_G(\varphi)|=m\). Then there is a \(\varphi\)-invariant nilpotent subgroup \(H\) and the index \(G:H\) is an \((r,m)\)-bounded number and the nilpotency class of \(H\) is an \(r\)-bounded number. If \(m=1\) then the group \(G\) is a nilpotent group of \(r\)-bounded nilpotency class.