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Bicyclic units of $\mathbb{Z} S_n$

Author(s): Aurora Olivieri; Ángel del Río
Journal: Proc. Amer. Math. Soc. 131 (2003), 1649-1653.
MSC (2000): Primary 20C05; Secondary 16U60
Posted: January 15, 2003
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Abstract: 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:

1.: P.J. Allen and C. Hobby, A characterization of units of $\mathbb{Z} S_4$ , Comm. in Algebra 16 (1988), 1479-1505. MR 89g:20005
2.: H. Bass, J. Milnor and J.P. Serre Solution of the congruence subgroup problem for ${SL}_n (n\ge 3)$ and ${\rm Sp}_{2n} (n\ge 2)$ , Publ. Math. IHES 33 (1967), 59-137. MR 39:5574
3.: E. Jespers and M.M. Parmenter, Bicyclic units in $\mathbb{Z} S_3$ , Bull. Belg. Math. Soc. 44 (1992), 141-146. MR 95j:16035
4.: A.J. Hahn and O.T. O'Meara, The classical groups and K-Theory, Springer-Verlag, 1989. MR 90i:20002
5.: S.K. Sehgal, Units of integral group rings, Longman Scientific and Technical Essex, 1993. MR 94m:16039

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Additional Information:

Aurora Olivieri
Affiliation: Departamento de Matemáticas, Universidad Simón Bolívar, Apartado Postal 89000, Caracas 1080-A, Venezuela
Email: olivieri@usb.ve

Ángel del Río
Affiliation: Departamento de Matemáticas, Universidad de Murcia, 30100 Murcia, Spain
Email: adelrio@um.es

DOI: 10.1090/S0002-9939-03-06839-4
PII: S 0002-9939(03)06839-4
Received by editor(s): May 16, 2001
Received by editor(s) in revised form: July 17, 2001
Posted: January 15, 2003
Additional Notes: The second author was partially supported by the D.G.I. of Spain and Fundación Séneca of Murcia.
Communicated by: Stephen D. Smith
Copyright of article: Copyright 2003, American Mathematical Society


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