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Lie Solvable Group Rings

Published online by Cambridge University Press:  20 November 2018

I. B. S. Passi ,
D. S. Passman  and
S. K. Sehgal
I. B. S. Passi
Affiliation:
Kurukshetra University, Kurukshetra, India
D. S. Passman
Affiliation:
University of Wisconsin, Madison, Wisconsin
S. K. Sehgal
Affiliation:
University of Alberta, Edmonton, Alberta
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Let K[G] denote the group ring of G over the field K. One of the interesting problems which arises in the study of such rings is to find precisely when they satisfy polynomial identities. This has been solved for char K = 0 in [1] and for char K = p > 0 in [3]. The answer is as follows. If p > 0 we say that group A is p-abelian if A', the commutator subgroup of A, is a finite p-group. Moreover, for convenience, we say A is 0-abelian if and only if it is abelian.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 4 , August 1973 , pp. 748 - 757
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Isaacs, I. M. and Passman, D. S., Groups with representations of bounded degree, Can. J. Math. 16 (1964), 299–309.Google Scholar
2. Passman, D. S., Infinite group rings (Marcel Dekker, New York, 1971).Google Scholar
3. Passman, D. S., Group rings satisfying a polynomial identity, J. Algebra 20 (1972), 103–117.Google Scholar
4. Passman, D. S., Group rings satisfying a polynomial identity. Ill, Proc. Amer. Math. Soc. 31 (1972), 87–90.Google Scholar