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Bicyclic Units in some Integral Group Rings

  • E. Jespers (a1)

Abstract

A description is given of the unit group for the two groups G = D 12 and G = D 8 × C 2. In particular, it is shown that in both cases the bicyclic units generate a torsion-free normal complement. It follows that the Bass-cyclic units together with the bicyclic units generate a subgroup of finite index in for all n ≥ 3.

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References

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1. Cliff, G. H., Sehgal, S. K. and Weiss, A. R., Units of integral group rings of metabelian groups, J. Algebra (1)73(1981), 167185.
2. Jespers, E. and Leal, G., Describing units of integral group rings of some 2-groups, Comm. Algebra (6) 19(1991), 18091827.
3. Jespers, E. and Parmenter, M. M., Bicyclic units in ZS3 , Bull. Soc. Math. Belg. Sér. B. (2) 44(1992), 141145.
4. Jespers, E., Units of group rings of groups of order 16, Glasgow Math. J. 35(1993), 367379.
5. Newman, M., Integral matrices, Academic Press, New York, 1972.
6. Sehgal, S. K.,Topics in group rings, Marcel Dekker, New York, 1978.
7. Sehgal, S. K., Units of Integral Group Rings, Longman Scientific and Technical, Essex, 1993.
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Bicyclic Units in some Integral Group Rings

  • E. Jespers (a1)

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