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)



On groups with a central automorphism of infinite order

Authors: Martyn R. Dixon and M. J. Evans
Journal: Proc. Amer. Math. Soc. 114 (1992), 331-336
MSC: Primary 20F28; Secondary 20E36
MathSciNet review: 1072334
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that a group $ G$, whose center has finite exponent, has a central automorphism of infinite order if and only if $ G$ has an infinite abelian direct factor. It is also shown that the group of central automorphisms of a nilpotent $ p$-group of infinite exponent contains an uncountable torsionfree abelian subgroup

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

  • [1] J. Buckley and J. Wiegold, On the number of outer automorphisms of an infinite nilpotent $ p$-group, Arch. Math. 31 (1978), 321-328. MR 522855 (80k:20033)
  • [2] M. Curzio, D. J. S. Robinson, H. Smith, and J. Wiegold, Some remarks on central automorphisms of hypercentral groups, Arch. Math. 53 (1989), 327-331. MR 1015995 (90h:20053)
  • [3] S. Franciosi and F. de Giovanni, On torsion groups with nilpotent automorphism groups, Comm. Algebra 14 (1986), 1909-1935. MR 864563 (88b:20049)
  • [4] L. Fuchs, Infinite abelian groups, vol. 1, Academic Press, New York and London, 1970. MR 0255673 (41:333)
  • [5] F. Menegazzo and S. E. Stonehewer, On the automorphism group of a nilpotent $ p$-group, J. London Math. Soc. (2) 31 (1985), 272-276. MR 809948 (87c:20072)
  • [6] M. R. Pettet, Central automorphisms of periodic groups, Arch. Math. 51 (1988), 20-33. MR 954064 (90a:20057)
  • [7] D. J. S. Robinson, Applications of cohomology to the theory of groups, Groups-St. Andrews 1981, London Mathematical Society Lecture Note series, vol. 71, Cambridge Univ. Press, Cambridge, 1982. MR 679154 (84d:20052)
  • [8] A. E. Zaleskiĭ, A nilpotent $ p$-group has an outer automorphism, Dokl. Akad. Nauk SSSR 196 (1971); Soviet Math. Dokl. 12 (1971), 227-230.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 20F28, 20E36

Retrieve articles in all journals with MSC: 20F28, 20E36

Additional Information

Article copyright: © Copyright 1992 American Mathematical Society

American Mathematical Society