Back to Search
Start Over
INTERPLAY BETWEEN THE ALGEBRAIC STRUCTURE OF A GROUP AND ARITHMETIC PROPERTIES OF ITS SPECTRUM
- Source :
- International Journal of Algebra and Computation. 14:1-34
- Publication Year :
- 2004
- Publisher :
- World Scientific Pub Co Pte Lt, 2004.
-
Abstract
- We investigate the interplay between the algebraic structure of a group G and arithmetic properties of its spectrum σ(G) which consists of the eigenvalues of all the inner automorphisms of G. A complex number λ is called an eigenvalue of a group automorphism A:G→G if φ◦A|H=λ·φ for some non-trivial homomorphism [Formula: see text] defined on an A-invariant subgroup H⊂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.
Details
- ISSN :
- 17936500 and 02181967
- Volume :
- 14
- Database :
- OpenAIRE
- Journal :
- International Journal of Algebra and Computation
- Accession number :
- edsair.doi...........09a00b599f43cfccc8f8476dfe640d37