Gill, Nick
(2013).

PDF (Accepted Manuscript)
 Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Download (454kB)  Preview 
DOI (Digital Object Identifier) Link:  https://doi.org/10.1112/jlms/jdt010 

Google Scholar:  Look up in Google Scholar 
Abstract
Let G be a (2, m, n)group and let x be the number of distinct primes dividing χ, the Euler characteristic of G. We prove, first, that, apart from a finite number of known exceptions, a non abelian simple composition factor T of G is a finite group of Lie type with rank n ≤ x. This result is proved using new results connecting the prime graph of T to the integer x.
We then study the particular cases x = 1 and x = 2. We give a general structure statement for (2, m, n)groups which have Euler characteristic a prime power, and we construct an infinite family of these objects. We also give a complete classification of those (2, m, n)groups which are almost simple and for which the Euler characteristic is a prime power (there are four such).
Finally we announce a result pertaining to those (2, m, n)groups which are almost simple and for which χ is a product of two prime powers. All such groups which are not isomorphic to PSL2 (q) or PGL2 (q) are completely classified.
Item Type:  Journal Item 

Copyright Holders:  2013 London Mathematical Society 
ISSN:  14697750 
Academic Unit/School:  Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics Faculty of Science, Technology, Engineering and Mathematics (STEM) 
Related URLs:  
Item ID:  36570 
Depositing User:  Nick Gill 
Date Deposited:  12 Feb 2013 10:05 
Last Modified:  07 Dec 2018 15:05 
URI:  http://oro.open.ac.uk/id/eprint/36570 
Share this page: 
Metrics
Altmetrics from Altmetric  Citations from Dimensions 
Download history for this item
These details should be considered as only a guide to the number of downloads performed manually. Algorithmic methods have been applied in an attempt to remove automated downloads from the displayed statistics but no guarantee can be made as to the accuracy of the figures.