The automorphism group of a near-ring
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- by S. D. Scott PDF
- Proc. Amer. Math. Soc. 80 (1980), 560-562 Request permission
Abstract:
As for groups certain automorphisms of a near-ring N may be regarded as inner. The inner automorphisms of N form a normal subgroup of the automorphism group of N. Let V be a group, $\Lambda$ the automorphism group of V, and N the near-ring of maps of V into V generated by $\Lambda$. It is shown that if $\Lambda$ is a complete group (see [2, p. 94]), then it frequently happens that the automorphisms of N are all inner. Using this result the automorphism groups of certain near-rings may be found.References
- Günter Pilz, Near-rings, North-Holland Mathematics Studies, No. 23, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1977. The theory and its applications. MR 0469981
- Eugene Schenkman, Group theory, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1965. MR 0197537
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 80 (1980), 560-562
- MSC: Primary 16A76; Secondary 20F28
- DOI: https://doi.org/10.1090/S0002-9939-1980-0587927-2
- MathSciNet review: 587927