Result: A RECOGNITION OF SIMPLE GROUPS PSL (3, q ) BY THEIR ELEMENT ORDERS: A recognition of simple groups \(\text{PSL}(3,q)\) by their element orders.
Title:
A RECOGNITION OF SIMPLE GROUPS PSL (3, q ) BY THEIR ELEMENT ORDERS: A recognition of simple groups \(\text{PSL}(3,q)\) by their element orders.
Source:
Acta Mathematica Scientia. 24:45-51
Publisher Information:
Elsevier BV, 2004.
Publication Year:
2004
Subject Terms:
sets of element orders, recognizable groups, spectra, 4. Education, Simple groups: alternating groups and groups of Lie type, 0102 computer and information sciences, 0101 mathematics, projective special linear groups, 01 natural sciences, Arithmetic and combinatorial problems involving abstract finite groups
Document Type:
Academic journal
Article
File Description:
application/xml
Language:
English
ISSN:
0252-9602
DOI:
10.1016/s0252-9602(17)30358-2
Rights:
Elsevier TDM
Accession Number:
edsair.doi.dedup.....e7da3218a920f5865b3729f3d5a262dd
Database:
OpenAIRE
Further Information
For a finite group \(G\), let \(\pi_e(G)\) be the spectrum of \(G\), i.e. the subset of the set of natural numbers consisting of the orders of elements in \(G\). A group \(G\) is said to be recognizable (by the spectrum) if every finite group \(H\) with \(\pi_e(H)=\pi_e(G)\) is isomorphic to \(G\). The authors prove that the finite simple group \(L_3(q)\) is recognizable if \(3