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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 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Rings generated by the inner-automorphisms of non-abelian groups
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by A. John Chandy PDF
Proc. Amer. Math. Soc. 30 (1971), 59-60 Request permission

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
  • A. Fröhlich, The near-ring generated by the inner automorphisms of a finite simple group, J. London Math. Soc. 33 (1958), 95–107. MR 93543, DOI 10.1112/jlms/s1-33.1.95
  • A. Fröhlich, Distributively generated near-rings. I. Ideal theory. II. Representation theory, Proc. London Math. Soc. (3) 8 (1958), 76–94, 95–108. MR 92774, DOI 10.1112/plms/s3-8.1.76
  • F. W. Levi, Groups in which the commutator operation satisfies certain algebraic conditions, J. Indian Math. Soc. (N.S.) 6 (1942), 87–97. MR 7417
  • 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
  • © Copyright 1971 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 30 (1971), 59-60
  • MSC: Primary 16.10; Secondary 20.00
  • DOI: https://doi.org/10.1090/S0002-9939-1971-0280519-9
  • MathSciNet review: 0280519