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Involutions and free pairs of bicyclic units in integral group rings.
- Source :
-
Journal of Group Theory . Sep2010, Vol. 13 Issue 5, p721-742. 22p. - Publication Year :
- 2010
-
Abstract
- If * : G → G is an involution on the finite group G, then * extends to an involution on the integral group ring ℤ[ G]. In this paper, we consider whether bicyclic units u ∈ ℤ[ G] exist with the property that the group 〈 u, u*〉 generated by u and u* is free on the two generators. If this occurs, we say that ( u, u*) is a free bicyclic pair. It turns out that the existence of u depends strongly upon the structure of G and on the nature of the involution. One positive result here is that if G is a nonabelian group with all Sylow subgroups abelian, then for any involution *, ℤ[ G] contains a free bicyclic pair. [ABSTRACT FROM AUTHOR]
- Subjects :
- *FINITE groups
*ALGEBRA
*GROUP theory
*MATHEMATICS
*FINITE element method
Subjects
Details
- Language :
- English
- ISSN :
- 14335883
- Volume :
- 13
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- Journal of Group Theory
- Publication Type :
- Academic Journal
- Accession number :
- 53482240
- Full Text :
- https://doi.org/10.1515/JGT.2010.019