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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.

References [Enhancements On Off] (What's this?)

  • [1] Günter Pilz, Near-rings, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1977. The theory and its applications; North-Holland Mathematics Studies, No. 23. MR 0469981
  • [2] Eugene Schenkman, Group theory, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1965. MR 0197537

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Article copyright: © Copyright 1980 American Mathematical Society

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