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On the concept of length in the sense of Lausch-Nöbauer and its generalizations

Part of: Other generalizations of groups

Published online by Cambridge University Press:  09 April 2009

Günther Eigenthaler  and
Johann Wiesenbauer
Johann Wiesenbauer
Affiliation:
Institut für Algebra und Mathematische Strukturtheorie, Technische Universität Wien Argentinierstrasse 8, A-1040 Wien Austria
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Abstract

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In this paper the concept of length as defined for groups by Lausch–Nöbauer in their book Algebra of Polynomials (North Holland, Amsterdam, 1973) is generalized in several ways. It turns out that the main results of Lausch-Nöbauer concerning it remain valid for this generalization.

MSC classification

Secondary: 20N99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 24 , Issue 2 , September 1977 , pp. 162 - 169
Copyright
Copyright © Australian Mathematical Society 1977

References

Cohn, P. M. (1965), Universal Algebra (Harper and Row, New York, 1965).Google Scholar
Foster, A. L. (1955), “The identities of—and unique subdirect factorization within—classes of universal algebras”, Math. Z. 62, 171–188.Google Scholar
Froemke, J. (1971), “Pairwise and general independence of abstract algebras”, Math. Z. 123, 1–17.Google Scholar
Grätzer, G. (1968), Universal Algebra (Van Nostrand, Princeton, 1968).Google Scholar
Kuroš, A. G. (1963), Lectures on General Algebra (Chelsea Publishing Company, New York, 1963).Google Scholar
Lausch, H. and Nöbauer, W. (1973), Algebra of Polynomials (North Holland, Amsterdam, 1973).Google Scholar
Scott, S. D. (1969), “The arithmetic of polynomial maps over a group and the structure of certain permutational polynomial groups I”, Monatsh. Math. 73, 250–267.Google Scholar