Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Automorphisms of the integral group ring of $ S\sb{n}$


Author: Gary L. Peterson
Journal: Proc. Amer. Math. Soc. 59 (1976), 14-18
MSC: Primary 20C05
DOI: https://doi.org/10.1090/S0002-9939-1976-0412259-1
MathSciNet review: 0412259
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper it is shown that every normalized automorphism of the integral group ring of $ {S_n}$ can be written as a group automorphism followed by conjugation by a unit in the group algebra of $ {S_n}$ over the rationals.


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

  • [1] H. Boerner, Representations of groups, 2nd English ed., North-Holland, Amsterdam; American Elsevier, New York, 1970. MR 42 #7792. MR 0272911 (42:7792)
  • [2] C. F. Brown, Automorphisms of integral group rings, Ph. D. Thesis, Michigan State University, 1971.
  • [3] G. L. Peterson, Automorphisms of integral group rings. I Arch. Math. (to appear).
  • [4] -, Automorphisms of integral group rings. II (to appear).
  • [5] W. R. Scott, Group theory, Prentice-Hall, Englewood Cliffs, N. J., 1964. MR 29 #4785. MR 0167513 (29:4785)
  • [6] S. K. Sehgal, On the isomorphism of integral group rings. I, Canad. J. Math. 21 (1969), 410-413. MR 41 #366. MR 0255706 (41:366)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 20C05

Retrieve articles in all journals with MSC: 20C05


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0412259-1
Keywords: Integral group ring, symmetric group, normalized automorphism, group automorphism, augmentation, class sum
Article copyright: © Copyright 1976 American Mathematical Society

American Mathematical Society