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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Near-rings of invariants. II


Author: C. J. Maxson
Journal: Proc. Amer. Math. Soc. 117 (1993), 27-35
MSC: Primary 16Y30; Secondary 20B99
DOI: https://doi.org/10.1090/S0002-9939-1993-1126199-6
MathSciNet review: 1126199
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Abstract: Let $ E$ be the equivalence relation determined by the orbits of a group $ G$ acting on a set $ X$ and let $ K$ be a group. Using a "sandwich" function $ \varphi :X/E \to K,\;M(X,G,K,\varphi ) = \{ f:X \to K\vert f\;{\text{is constant on each}}\;E{\text{-class}}\} $ is a near-ring, the near-ring of invariants determined by $ (X,G,K,\varphi )$. In this paper we continue the study of the transfer of information between the structure of the near-ring of invariants and properties of the group action $ (G,X)$, the group $ K$, and the function $ \varphi :K \to X/E$.


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DOI: https://doi.org/10.1090/S0002-9939-1993-1126199-6
Article copyright: © Copyright 1993 American Mathematical Society