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On the finiteness and uniqueness of certain 2-tame N-groups

Published online by Cambridge University Press:  20 January 2009

S. D. Scott
S. D. Scott
Affiliation:
Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand
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Abstract

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Unlike ring modules certain faithful N-groups are unique. The main theorem is that if N is a 2-tame ring-free near-ring where N/J(N) has DCCR, then all faithful 2-tame N-groups are finite and N-isomorphic. The finiteness of such an N-group follows easily from the fact it has a composition series. It is then shown that the length of a composition series depends only on N. This fact is used at key points in the proof. The situations where the N-group has or has not a minimal submodule require different analysis. The first case makes use of other interesting results and the second makes strong use of the inductive assumption.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 38 , Issue 2 , June 1995 , pp. 193 - 205
Copyright
Copyright © Edinburgh Mathematical Society 1995

References

REFERENCES

1.Curtis, C. W. and Reiner, I., Representation Theory of Finite Groups and Associative Algebras (Interscience Publishers, New York 1966).Google Scholar
2.Meldrum, J. D. P., Near-rings and their Links with Groups (Pitman Publishing, London (1985).Google Scholar
3.Pilz, G., Near-rings (North-Holland, Amsterdam 1983).Google Scholar
4.Scott, S. D., Linear Ω-groups, polynomial maps, Contr. Gen. Alg. 8 (1991), 239–293.Google Scholar
5.Scott, S. D., Tame near-rings and N-groups, Proc. Edinburgh Math. Soc. 23 (1980), 275–296.CrossRefGoogle Scholar
6.Scott, S. D., Tame Theory, unpublished booklet.Google Scholar