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

 

Rings generated by the inner-automorphisms of non-abelian groups


Author: A. John Chandy
Journal: Proc. Amer. Math. Soc. 30 (1971), 59-60
MSC: Primary 16.10; Secondary 20.00
MathSciNet review: 0280519
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Abstract: The endomorphisms of an abelian group form a ring. The characterization of groups in which endomorphisms generate a ring is still an open question. It is shown here that the inner-automorphisms of a group generate a ring if and only if the conjugate elements in the group commute.


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

  • [1] A. Fröhlich, The near-ring generated by the inner automorphisms of a finite simple group, J. London Math. Soc. 33 (1958), 95–107. MR 0093543 (20 #67)
  • [2] A. Fröhlich, Distributively generated near-rings. I. Ideal theory. II. Representation theory, Proc. London Math. Soc. (3) 8 (1958), 76–94, 95–108. MR 0092774 (19,1156b)
  • [3] F. W. Levi, Groups in which the commutator operation satisfies certain algebraic conditions, J. Indian Math. Soc. (N.S.) 6 (1942), 87–97. MR 0007417 (4,133i)
  • [4] F. Levi and B. L. Van der Waerden, Über eine besondere Klasse von Gruppen, Abh. Math. Sem. Univ. Hamburg 9 (1933), 154-158.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0280519-9
PII: S 0002-9939(1971)0280519-9
Keywords: Nilpotent groups, near-rings, inner-automorphisms
Article copyright: © Copyright 1971 American Mathematical Society