Bicyclic units of ℤ𝕊_{𝕟}

Bicyclic units of $\mathbb {Z} S_n$
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Proc. Amer. Math. Soc. 131 (2003), 1649-1653

DOI: https://doi.org/10.1090/S0002-9939-03-06839-4

Published electronically: January 15, 2003

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We prove that the group generated by the bicyclic units of $\mathbb {Z} S_n$ has torsion for $n\ge 4$. This answers a question of Sehgal (1993).

References

P. J. Allen and C. Hobby, A characterization of units in $\textbf {Z}S_4$, Comm. Algebra 16 (1988), no. 7, 1479–1505. MR 941181, DOI 10.1080/00927878808823639
H. Bass, J. Milnor, and J.-P. Serre, Solution of the congruence subgroup problem for $\textrm {SL}_{n}\,(n\geq 3)$ and $\textrm {Sp}_{2n}\,(n\geq 2)$, Inst. Hautes Études Sci. Publ. Math. 33 (1967), 59–137. MR 244257
E. Jespers and M. M. Parmenter, Bicyclic units in $\textbf {Z}S_3$, Bull. Soc. Math. Belg. Sér. B 44 (1992), no. 2, 141–146. MR 1313860
Alexander J. Hahn and O. Timothy O’Meara, The classical groups and $K$-theory, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 291, Springer-Verlag, Berlin, 1989. With a foreword by J. Dieudonné. MR 1007302, DOI 10.1007/978-3-662-13152-7
S. K. Sehgal, Units in integral group rings, Pitman Monographs and Surveys in Pure and Applied Mathematics, vol. 69, Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1993. With an appendix by Al Weiss. MR 1242557