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On the normaliser problem for G-adapted group rings of torsion groups

Published online by Cambridge University Press:  17 April 2009

Yuanlin Li
Yuanlin Li
Affiliation:
Department of Mathematics, Brock University, 500 Glenridge Ave., St. Catharines, Ontario, LZS 3A1 Canada, e-mail: [email protected]
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Abstract

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In this note, we prove that if a torsion group G has an Abelian subgroup B such that G/B is Abelian and R is a G-adapted ring with the property that R (G/B) has only trivial units then G has the normaliser property in RG.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 67 , Issue 1 , February 2003 , pp. 171 - 176
Copyright
Copyright © Australian Mathematical Society 2003

References

REFERENCES

[1]Hertweck, M., ‘A counterexample to the isomorphism problem for integral group rings’, Ann. of Math. 154 (2001), 115–138.CrossRefGoogle Scholar
[2]Hertweck, M., ‘Class-preserving automorphisms of finite groups’, J. Algebra 241 (2001), 1–26.CrossRefGoogle Scholar
[3]Hertweck, M. and Kimmerle, W., ‘Coleman automorphisms of finite groups’, Math. Z. 242 (2002), 203–215.CrossRefGoogle Scholar
[4]Higman, G., ‘The units of group rings’, Proc. London Math. Soc. (2) 46 (1940), 231–248.CrossRefGoogle Scholar
[5]Jackowski, S. and Marciniak, Z., ‘Group automorphisms inducing the identity map on cohomology’, J. Pure Appl. Algebra 44 (1987), 241–250.CrossRefGoogle Scholar
[6]Jespers, E., Juriaans, S.O., de Miranda, M. and Rogerio, J.R., ‘On the normalizer problem’, J. Algebra 247 (2002), 24–36.CrossRefGoogle Scholar
[7]Kegel, O.H. and Wehrfritz, B.A.F., Locally finite groups (North-Holland, Amsterdam, London, 1973).Google Scholar
[8]Kimmerle, W., ‘On the normalizer problem’, in Algebra, Trends in Math. (Birkhauser, Basel, 1999), pp. 89–98.Google Scholar
[9]Li, Y., ‘The normalizer of a metabelian group in its integral group ring’, J. Algebra (2002) (to appear).CrossRefGoogle Scholar
[10]Li, Y., Paramenter, M.M. and Sehgal, S.K., ‘On the normalizer property for integral group rings’, Comm. Algebra 27 (1999), 4217–4223.CrossRefGoogle Scholar
[11]Marciniak, Z.S. and Roggenkamp, K.W., ‘The normalizer of a finite group in its integral group ring and Čech cohomology’, in Algebra - Representation Theory, 2001 (Kluwer Academic Publishers, 2001), pp. 159–188.Google Scholar
[12]Mazur, M., ‘Automorphisms of finite groups’, Comm. Algebra 22 (1994), 6259–6271.CrossRefGoogle Scholar
[13]Mazur, M., ‘On the isomorphism problem for integral group rings of infinite groups’, Exposition. Math. 13 (1995), 433–445.Google Scholar
[14]Mazur, M., ‘The normalizer of a group in the unit group of its group ring’, J. Algebra 212 (1999), 175–189.CrossRefGoogle Scholar
[15]Sehgal, S.K., Units in integral group rings, Pitman Monographs in Pure and Applied Maths. 69 (Longman Scientific and Technical, Harlow, 1993).Google Scholar