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Hypercentral Units in Alternative Integral Loop Rings

✍ 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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πŸ“œ SIMILAR VOLUMES


Units in Integral Loop Rings
✍ Luiz G.X. de Barros; Stanley O. Juriaans πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 161 KB

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.

Alternative Loop Rings with Solvable Uni
✍ Edgar G Goodaire; CΓ©sar Polcino Milies πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 129 KB

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.

Gauss Units in Integral Group Rings
✍ Olaf Neisse; Sudarshan K. Sehgal πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 147 KB
Products of Free Groups in the Unit Grou
✍ Eric Jespers; Guilherme Leal; Angel del RΔ±́o πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 253 KB

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

Products of Free Groups in the Unit Grou
✍ Guilherme Leal; Angel del Rı́o πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 221 KB

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 Ž groups. This completes the work of Jespers, Leal, and del Rıo J. Algebra 180 Ž . . 1996 , 22᎐40 , where the nilpotent groups with