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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The automorphism group of a near-ring


Author: S. D. Scott
Journal: Proc. Amer. Math. Soc. 80 (1980), 560-562
MSC: Primary 16A76; Secondary 20F28
MathSciNet review: 587927
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1980-0587927-2
PII: S 0002-9939(1980)0587927-2
Article copyright: © Copyright 1980 American Mathematical Society