Central units of integral group rings

of nilpotent groups

Authors:
E. Jespers, M. M. Parmenter and S. K. Sehgal

Journal:
Proc. Amer. Math. Soc. **124** (1996), 1007-1012

MSC (1991):
Primary 16U60, 20C05, 20C07; Secondary 20C10, 20C12

MathSciNet review:
1328353

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper a finite set of generators is given for a subgroup of finite index in the group of central units of the integral group ring of a finitely generated nilpotent group.

**1.**Hyman Bass,*The Dirichlet unit theorem, induced characters, and Whitehead groups of finite groups*, Topology**4**(1965), 391–410. MR**0193120****2.**Jürgen Ritter and Sudarshan K. Sehgal,*Integral group rings with trivial central units*, Proc. Amer. Math. Soc.**108**(1990), no. 2, 327–329. MR**994785**, 10.1090/S0002-9939-1990-0994785-7**3.**Jürgen Ritter and Sudarshan K. Sehgal,*Construction of units in integral group rings of finite nilpotent groups*, Trans. Amer. Math. Soc.**324**(1991), no. 2, 603–621. MR**987166**, 10.1090/S0002-9947-1991-0987166-9**4.**Jürgen Ritter and Sudarshan K. Sehgal,*Units of group rings of solvable and Frobenius groups over large rings of cyclotomic integers*, J. Algebra**158**(1993), no. 1, 116–129. MR**1223670**, 10.1006/jabr.1993.1126**5.**Derek John Scott Robinson,*A course in the theory of groups*, Graduate Texts in Mathematics, vol. 80, Springer-Verlag, New York-Berlin, 1982. MR**648604****6.**Sudarshan K. Sehgal,*Topics in group rings*, Monographs and Textbooks in Pure and Applied Math., vol. 50, Marcel Dekker, Inc., New York, 1978. MR**508515****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**

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Additional Information

**E. Jespers**

Affiliation:
Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, Newfoundland, Canada A1C 5S7

Email:
ejespers@albert.math.mun.ca

**M. M. Parmenter**

Affiliation:
Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, Newfoundland, Canada A1C 5S7

Email:
mparmen@plato.ucs.mun.ca

**S. K. Sehgal**

Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Alberta, Canada T6G 2G1

Email:
ssehgal@schur.math.ualberta.ca

DOI:
http://dx.doi.org/10.1090/S0002-9939-96-03398-9

Received by editor(s):
August 4, 1994

Additional Notes:
This work is supported in part by NSERC Grants OGP0036631, A8775 and A5300, Canada, and by DGICYT, Spain

Communicated by:
Ronald Solomon

Article copyright:
© Copyright 1996
American Mathematical Society