Keywords
- Normal Subgroup
- Nilpotent Group
- Group Ring
- Nilpotent Class
- Canonical Homomorphism
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
J.C. Ault and J.F. Watters, "Circle groups of nilpotent rings", Amer. Math. Monthly 80 (1973), pp. 48–52, MR47:5040.
H.A. Bender, "A determination of the groups of order p 5", Ann. of Math. (2) 29 (1927), pp. 61–72, FdM53, p. 105.
A.W. Hales and I.B.S. Passi, "The second augmentation quotient of an integral group ring", Arch. Math. 31 (1978), pp. 259–265, MR81a:20010.
R.L. Kruse and D.T. Price, Nilpotent Rings (Gordon and Breach, New York, London, Paris, 1969), MR42:1858.
F. Röhl and J. Ullrich, "Über Komplettierungen und Lokalisierungen von Zirkelgruppen nilpotenter Ringe", Arch. Math. 37 (1981), pp. 300–305, MR83j:17002.
R. Sandling, "Group rings of circle and unit groups", Math. Z. 140 (1974), pp. 195–202, MR52:3217.
R. Sandling and K. Tahara, "Augmentation quotients of group rings and symmetric powers", Math. Proc. Camb. Philos. Soc. 85 (1979), pp. 247–252, MR80h:20014.
K. Tahara, "On the structure of Q 3(G) and the fourth dimension subgroups", Japan. J. Math. (New Series) 3 (1977), pp. 381–394, MR58:28157.
K. Tahara, "The augmentation quotients of group rings and the fifth dimension subgroups", J. Algebra 71 (1981), pp. 141–173, MR83b:20007.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1984 Springer-Verlag
About this paper
Cite this paper
Tahara, KI., Hosomi, A. (1984). On the circle groups of finite nilpotent rings. In: Kim, A.C., Neumann, B.H. (eds) Groups — Korea 1983. Lecture Notes in Mathematics, vol 1098. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099672
Download citation
DOI: https://doi.org/10.1007/BFb0099672
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-13890-7
Online ISBN: 978-3-540-39102-9
eBook Packages: Springer Book Archive
