Abstract
The object of this note is the structure of the normalizer of a group basis of the group ring RG of a finite group G, where R = Z or more generally in the situation when R is G-adapted. This means that R is an integral domain of characteristic zero in which no prime divisor of |G| is invertible.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Arora, S. R. and Passi, I. B. S. Central height of the unit group of an integral group ring, Comm. Alg., 21, 3673–3683, 1993.
Conway, J. H. Curtis, R. T. Norton, S. P. Parker, R. A. and Wilson, R. A. Atlas of Finite Groups, Oxford University Press, London/New York, 1985.
Feit, W. and Seitz, G. M. On finite rational groups and related topics, Illinois J. Math., 33, No.1, 103–131, 1988.
Gross, F. Automorphisms which centralize a Sylow p-subgroup, J. Alg., 77, 202–233, 1982.
Hertweck, M. Eine Lösung des Isomorphieproblems für ganzzahlige Gruppenringe von endlichen Gruppen. Dissertation, Universität Stuttgart, 1998.
Jackowski S. and Marciniak, Z. Group automorphisms inducing the identity map on cohomology, J. p. appl. Alg., 44, 241–250, 1987.
Kimmerle, W. On automorphisms of ZG and the Zassenhaus conjectures, CMS Conf. Proc., 18, 383–397, 1996.
Kimmerle, W. Lyons, R. Sandling, R. and Teague, D. Composition factors from the group ring and Artin’s theorem on orders of simple groups, Proc. London Math. Soc., 60(3), 89–122, 1990.
Kimmerle, W. and Roggenkamp, K. W. Projective limits of group rings, J. pure appl. Alg., 88, 119–142, 1993.
Mazur, M. On the isomorphism problem for infinite group rings, Expositiones Mathematicae, Spektrum Akademischer Verlag (Heidelberg) 13, 433–445, 1995.
Parmenter, M. Talk given at Groups 97 in Bath, England.
Ritter, J. and Sehgal, S. K. Integral group rings with trivial central units, Proc. AMS 108, Nr. 2, 327–329, 1990.
Roggenkamp, K. W. The isomorphism problem for integral group rings of finite groups, Proc. int. Cong. Math., Kyoto 1990, Springer 369–380, 1991.
Roggenkamp, K. W. and Scott, L. L. Isomorphisms of p-adic group rings, Ann. Math., 126, 593–647, 1987.
Roggenkamp, K. W. and Zimmermann, A. Outer group automorphisms may become inner in the integral group ring, J. pure appl. Alg., 103, 91–99, 1995a.
Roggenkamp, K. W. and Zimmermann, A. A counterexample for the isomorphism problem of polycyclic groups. J. pure appl. Alg., 103, 101–103, 1995b.
Sandling, R. The isomorphism problem for group rings, a survey, Lect. Not. Math., Nr. 1148, Springer 256–289, 1985.
Sehgal S. K. Units in Integral Group Rings, Longman Scientific and Technical, Essex, 1993.
Scott, L. L. Recent Progress on the Isomorphism Problem, Proc. Symp. pure Math., 47, 259–274, 1987.
Weiss, A. p-adic rigidity of p-torsion, Ann. Math., 127, 317–332, 1987.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Hindustan Book Agency (India) and Indian National Science Academy
About this chapter
Cite this chapter
Kimmerle, W. (1999). On the Normalizer Problem. In: Passi, I.B.S. (eds) Algebra. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9996-3_6
Download citation
DOI: https://doi.org/10.1007/978-3-0348-9996-3_6
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0348-9998-7
Online ISBN: 978-3-0348-9996-3
eBook Packages: Springer Book Archive