Torsion Units in Integral Group Rings
Canadian mathematical bulletin, Tome 38 (1995) no. 3, pp. 317-324

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

Special cases of Bovdi's conjecture are proved. In particular the conjecture is proved for supersolvable and Frobenius groups. We also prove that if is finite, α ∊ VZG a torsion unit and m the smallest positive integer such that αm ∊ G then m divides .
DOI : 10.4153/CMB-1995-046-7
Mots-clés : 20C05, 20C07, 16S34, 16U60, group rings, torsion units, generalized trace
Juriaans, Stanley Orlando. Torsion Units in Integral Group Rings. Canadian mathematical bulletin, Tome 38 (1995) no. 3, pp. 317-324. doi: 10.4153/CMB-1995-046-7
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[1] 1. Bovdi, A. A., The Unit Group of Integral Group Rings (Russian), Uzhgorod Univ. 21(1987), Dep. Ukr. Ninti 24.09.87, N2712-UK 87. Google Scholar

[2] 2. Bovdi, A., Marciniak, Z. and Sehgal, S. K., Torsion Units in Infinite Group Rings, J. Number Theory 47( 1994), 284–299. Google Scholar

[3] 3. Burnside, W., Theory of groups of finite order, 2nd edition, Dover Publication, Inc. Google Scholar

[4] 4. Dokuchaev, M. A., Torsion units in integral group ring ofnilpotent metabelian groups, Comm. Algebra (2) 20(1992), 423–435. Google Scholar

[5] 5. Gorenstein, D., Finite groups, Harper & Row Publisher, New York, 1968. Google Scholar

[6] 6. Juriaans, O. S., Torsion units in integral group ring, Comm. Algebra, to appear. Google Scholar

[7] 7. Isaacs, I. M., Character theory of finite groups, Academic Press, New York, San Francisco, London, 1976. Google Scholar

[8] 8. Luthar, I. S. and Poonam, T., Zassenhaus Conjecture for S5, preprint. Google Scholar

[9] 9. Marciniak, Z., Ritter, J., Sehgal, S. K. and A. Weiss, Torsion units in integral group rings of some metabelian groups, II, J. Number Theory 25(1987), 340–352. Google Scholar

[10] 10. Passman, D. S., Permutation groups, W. A. Benjamin, Inc., New York, 1968. Google Scholar

[11] 11. Robinson, D. J. S., A course in the theory of groups, Springer-Verlag, New York, Heidelberg, Berlin, 1980. Google Scholar

[12] 12. Scott, W. R., Group theory, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1964. Google Scholar

[13] 13. Suzuki, M., Group Theory II, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo, 1985. Google Scholar

[14] 14. Sehgal, S. K., Topics in group rings, Marcel Dekker, Inc., New York and Basel, 1978. Google Scholar

[15] 15. Sehgal, S. K., Units of Integral Group Rings, Longman's, Essex, 1993. Google Scholar

[16] 16. Weiss, A., Torsion units in integral group rings, J. Reine Angew. Math. 415(1991), 175–187 Google Scholar

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