Central units of the integral group ring

Authors:
Yuanlin Li and M. M. Parmenter

Journal:
Proc. Amer. Math. Soc. **125** (1997), 61-65

MSC (1991):
Primary 16U60, 20C05

DOI:
https://doi.org/10.1090/S0002-9939-97-03626-5

MathSciNet review:
1353390

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Abstract | References | Similar Articles | Additional Information

Abstract: There are very few cases known of nonabelian groups where the group of central units of , denoted , is nontrivial and where the structure of , including a complete set of generators, has been determined. In this note, we show that the central units of augmentation 1 in the integral group ring form an infinite cyclic group , and we explicitly find the generator .

**1.**E. Jespers, M.M. Parmenter and S.K. Sehgal, Central units of integral group rings of nilpotent groups. Proc. Amer. Math. Soc. 124 (1996), 1007-1012.**2.**Ivan Niven and H.S. Zuckerman,*An Introduction to the Theory of Numbers*(4th edition), Wiley, 1980. MR**81g:10001****3.**J. Ritter and S.K. Sehgal, Integral group rings with trivial central units, Proc. Amer. Math. Soc. 108 (1990), 327-329. MR**90d:16009****4.**J. Ritter and S.K. Sehgal, Construction of units in integral group rings of finite nilpotent groups, Trans. Amer. Math. Soc. 324(2) (1991), 603-621. MR**91h:20008****5.**J. Ritter and S.K. Sehgal, Units of group rings of solvable and Frobenius groups over large rings of cyclotomic integers, Journal of Algebra 158 (1993), 116-129. MR**95d:16045****6.**S.K. Sehgal,*Units in Integral Group Rings*, Longman, 1993. MR**94m:16039**

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Additional Information

**Yuanlin Li**

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

Email:
yuanlin@fermat.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

DOI:
https://doi.org/10.1090/S0002-9939-97-03626-5

Received by editor(s):
July 22, 1995

Additional Notes:
The second author was supported in part by NSERC grant A8775.

Communicated by:
Ronald M. Solomon

Article copyright:
© Copyright 1997
American Mathematical Society