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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Near-fields associated with invariant linear $\kappa$-relations
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by Peter Fuchs and C. J. Maxson
Proc. Amer. Math. Soc. 103 (1988), 729-736
DOI: https://doi.org/10.1090/S0002-9939-1988-0947647-6

Abstract:

In this paper we investigate a construction method for subnearrings of $M\left ( G \right )$ proposed by H. Wielandt using subgroups of direct powers ${G^\kappa }$ of $G$ called invariant linear $\kappa$-relations. If $\kappa = 2$ we characterize, in terms of properties of these subgroups, when the associated near-rings are near-fields and prove that every near-field arising from an invariant linear $2$-relation must be a field.
References
  • C. J. Maxson and J. D. P. Meldrum, Centralizer representations of near-fields, J. Algebra 89 (1984), no. 2, 406–415. MR 751153, DOI 10.1016/0021-8693(84)90226-6
  • J. D. P. Meldrum, Near-rings and their links with groups, Research Notes in Mathematics, vol. 134, Pitman (Advanced Publishing Program), Boston, MA, 1985. MR 854275
  • Günter Pilz, Near-rings, 2nd ed., North-Holland Mathematics Studies, vol. 23, North-Holland Publishing Co., Amsterdam, 1983. The theory and its applications. MR 721171
  • R. Remak, Über die Darstellung der endlichen Gruppen als Untergruppen direkter Produkte, J. Reine Angew. Math. 163 (1930), 1-44. —, Über Untergruppen direkter Produkte von drei Faktoren, J. Reine Angew. Math. 166 (1932), 65-100. H. Wielandt, Permutation groups through invariant relations and invariant functions, Lecture Notes, Ohio State University, Columbus, 1969. —, How to single out function near-rings, Oberwolfach Abstracts, 1972.
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Bibliographic Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 103 (1988), 729-736
  • MSC: Primary 16A76; Secondary 12K05, 20E99
  • DOI: https://doi.org/10.1090/S0002-9939-1988-0947647-6
  • MathSciNet review: 947647