Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-04T21:42:45.723Z Has data issue: false hasContentIssue false
  • English
  • Français

Augmentation quotients and dimension subgroups of semidirect products

Published online by Cambridge University Press:  24 October 2008

Ken-Ichi Tahara
Ken-Ichi Tahara
Affiliation:
Aichi University of Education, Kariya, Japan448
Get access Rights & Permissions [Opens in a new window]

Extract

Sandling(6) determined the dimension subgroups of the semidirect product of a normal abelian subgroup and a subgroup; namely if G = NT is the semidirect product of a normal abelian subgroup N and a subgroup T, then the mth dimension subgroup Dm(G) of G is equal to [N, (m – 1) G] · Dm (T) for all m ≧ 1, where

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 91 , Issue 1 , January 1982 , pp. 39 - 49
Copyright
Copyright © Cambridge Philosophical Society 1982

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Hall, M.The theory of groups (Macmillan Company, New York, 1959).Google Scholar
(2)Khambadkone, M. On the structure of augmentation ideals in group rings. (To appear.)Google Scholar
(3)Losey, G.N-series and filtrations of the augmentation ideai. Canad. J. Math. 26 (1974), 962–977.CrossRefGoogle Scholar
(4)Passi, I. B. S.Polynomial maps on groups. J. Algebra 9 (1968), 121–151.CrossRefGoogle Scholar
(5)Passi, I. B. S.Group rings and their augmentation ideals, Lecture Notes in Math., 715 (Springer-Verlag, Berlin-Heidelberg-New York, 1979).CrossRefGoogle Scholar
(6)Sandling, R.The dimension subgroup problem. J. Algebra 2 (1972), 216–231.CrossRefGoogle Scholar
(7)Sjogren, J. A.Dimension and lower central subgroups. J. Pure Appl. Algebra 14 (1979), 175–194.CrossRefGoogle Scholar
(8)Tahara, K.On the structure of Q 3(G) and the fourth dimension subgroups. Japan. J. Math., New Ser. 3 (1977), 381–394.CrossRefGoogle Scholar
(9)Tahara, K. The augmentation quotients of group rings and the fifth dimension svibgroups. J. Algebra. (In the Press.)Google Scholar