A note on the unit group of $\textbf {Z}S_ 3$
HTML articles powered by AMS MathViewer
- by P. J. Allen and C. Hobby PDF
- Proc. Amer. Math. Soc. 99 (1987), 9-14 Request permission
Abstract:
The group $V(Z{S_3})$ of units of augmentation 1 in $Z{S_3}$ is characterized as the group of all doubly stochastic matrices in ${\text {GL(}}3,Z)$. Two normal complements are presented, one of which is torsion free while the other contains elements of order 2.References
- P. J. Allen and C. Hobby, A characterization of units in $\textbf {Z}[A_{4}]$, J. Algebra 66 (1980), no. 2, 534–543. MR 593609, DOI 10.1016/0021-8693(80)90102-7
- G. H. Cliff, S. K. Sehgal, and A. R. Weiss, Units of integral group rings of metabelian groups, J. Algebra 73 (1981), no. 1, 167–185. MR 641639, DOI 10.1016/0021-8693(81)90353-7
- I. Hughes and K. R. Pearson, The group of units of the integral group ring $ZS_{3}$, Canad. Math. Bull. 15 (1972), 529–534. MR 325743, DOI 10.4153/CMB-1972-093-1 C. Milies, The units of the integral group ring $Z{D_4}$, Bol. Soc. Brasil. Mat. 4 (1972), 85-92.
- Morris Newman, Integral matrices, Pure and Applied Mathematics, Vol. 45, Academic Press, New York-London, 1972. MR 0340283
- D. S. Passman and P. F. Smith, Units in integral group rings, J. Algebra 69 (1981), no. 1, 213–239. MR 613869, DOI 10.1016/0021-8693(81)90139-3
- Olga Taussky, Matrices of rational integers, Bull. Amer. Math. Soc. 66 (1960), 327–345. MR 120237, DOI 10.1090/S0002-9904-1960-10439-9
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 99 (1987), 9-14
- MSC: Primary 20C05; Secondary 16A26, 20C10
- DOI: https://doi.org/10.1090/S0002-9939-1987-0866420-X
- MathSciNet review: 866420