Geodesic
Units of group rings of groups of order 16
Glasgow mathematical journal, Tome 35 (1993) no. 3, pp. 367-379

Voir la notice de l'article provenant de la source Cambridge University Press

Let G be a finite group, (ZG) the group of units of the integral group ring ZG and 1(ZG) the subgroup of units of augmentation 1. In this paper, we are primarily concerned with the problem of describing constructively (ZG) for particular groups G. This has been done for a small number of groups (see [11] for an excellent survey), and most recently Jespers and Leal [3] described (ZG) for several 2-groups. While the situation is clear for all groups of order less than 16, not all groups of order 16 were discussed in their paper. Our main aim is to complete the description of (ZG) for all groups of order 16. Since the structure of the unit group of abelian groups is very well known (see for example [10]), we are only interested in the non-abelian case. 
Jespers, E.; Parmenter, M. M. Units of group rings of groups of order 16. Glasgow mathematical journal, Tome 35 (1993) no. 3, pp. 367-379. doi: 10.1017/S0017089500009952
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[1] 1.Bass, H., The Dirichlet unit theorem, induced characters and Whitehead groups of finite groups, Topology 4 (1966), 391–410. Google Scholar | DOI

[2] 2.Cliff, G. H., Sehgal, S.K. and Weiss, A. R., Units of integral group rings of metabelian groups, J. Algebra 73 (1981), 167–185. Google Scholar | DOI

[3] 3.Jespers, E. and Leal, G., Describing units of integral group rings of some 2-groups, Comm. Algebra 19 (1991), 1809–1827. Google Scholar | DOI

[4] 4.Jespers, E., Leal, G. and Parmenter, M. M., Bicyclic and Bass cyclic units in group rings, Canad. Math. Bull. to appear. Google Scholar

[5] 5.Newman, M., Integral matrices (Academic Press, 1972). Google Scholar

[6] 6.Parmenter, M. M., Torsion-free normal complements in unit groups of integral group rings, C.R. Math. Rep. Acad. Sci. Canada 12 (1990), 113–118. Google Scholar

[7] 7.Pollard, H. and Diamond, H. G., The theory of algebraic numbers, The Carus Mathematical Monographs (Mathematical Association of America, 1975). Google Scholar | DOI

[8] 8.Ritter, J. and Sehgal, S. K., Generators of subgroups of U(ZG), Representation theory, group rings, and coding theory, Contemp. Math. 93 (Amer. Math. Soc., 1989), 331–347. Google Scholar | DOI

[9] 9.Ritter, J. and Sehgal, S. K., Construction of units in integral group rings of finite nilpotent groups, Trans. Amer. Math. Soc. 324 (1991), 603–621. Google Scholar | DOI

[10] 10.Sehgal, S. K., Topics in group rings (Marcel Dekker, 1978). Google Scholar

[11] 11.Sehgal, S. K., Units of integral group rings–A survey, preprint. Google Scholar

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