Paper Info
Title
Interplay Between The Algebraic Structure Of A Group And Arithmetic Properties Of Its Spectrum
Abstract
We investigate the interplay between the algebraic structure of a group G and arithmetic properties of its spectrum or(G) which consists of the eigenvalues of all the inner automorphisms of G. A complex number lambda is called an eigenvalue of a group automorphism A: G --> G if phi circle A\H = lambda (.) phi for some non-trivial homomorphism phi circle H --> C defined on an A-invariant subgroup H subset of G.It is shown that many properties of a group G (such as the presence of a finitely generated subgroup of infinite rank, nilpotence, periodicity, polycyclicity, etc.) are coded in its spectrum. In this paper the spectra are applied to the investigation of the so-called reversive properties of groups. The paper ends with a list of related open problems.
Year
DOI
Venue
2004
10.1142/S0218196704001645
INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION
Keywords
Field
DocType
eigenvalue of a group automorphism, spectrum of a group, free semigroup, virtually nilpotent group, collapsing group, solvable group, Hirsch rank
Characteristic subgroup,Cyclic group,p-group,Quaternion group,Discrete mathematics,Outer automorphism group,Combinatorics,Algebra,Automorphism,Arithmetic,Inner automorphism,Mathematics,Alternating group
Journal
Volume
Issue
ISSN
14
1
0218-1967
Citations 
PageRank 
References 
1
0.63
0
Authors
1
Name
Order
Citations
PageRank
Taras O. Banakh197.24