Higman has proved a classical result giving necessary and sufficient conditions for the units of an integral group ring to be trivial. In this paper we extend this result to loop rings of some diassociative loops.
Hypercentral Units in Alternative Integral Loop Rings
β Scribed by Ashwani K. Bhandari; Anjana Kaila
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 90 KB
- Volume
- 231
- Category
- Article
- ISSN
- 0021-8693
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π SIMILAR VOLUMES
Let L be an RA loop, that is, a loop whose loop ring in any characteristic is an alternative, but not associative, ring. We find necessary and sufficient conditions Ε½ . for the Moufang unit loop of RL to be solvable when R is the ring of rational integers or an arbitrary field.
We classify the nilpotent finite groups G which are such that the unit group Ε½ . U U ZG of the integral group ring ZG has a subgroup of finite index which is the direct product of noncyclic free groups. It is also shown that nilpotent finite groups having this property can be characterised by means
We classify all the finite groups G, such that the group of units of ZG contains a subgroup of finite index which is isomorphic to a direct product of nonabelian free Ε½ groups. This completes the work of Jespers, Leal, and del RΔ±o J. Algebra 180 Ε½ . . 1996 , 22α40 , where the nilpotent groups with