On groups with a central automorphism of infinite order
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- by Martyn R. Dixon and M. J. Evans
- Proc. Amer. Math. Soc. 114 (1992), 331-336
- DOI: https://doi.org/10.1090/S0002-9939-1992-1072334-7
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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 subgroupReferences
- Joseph Buckley and James Wiegold, On the number of outer automorphisms of an infinite nilpotent $p$-group, Arch. Math. (Basel) 31 (1978/79), no. 4, 321–328. MR 522855, DOI 10.1007/BF01226455
- Mario Curzio, Derek J. S. Robinson, Howard Smith, and James Wiegold, Some remarks on central automorphisms of hypercentral groups, Arch. Math. (Basel) 53 (1989), no. 4, 327–331. MR 1015995, DOI 10.1007/BF01195211
- Silvana Franciosi and Francesco de Giovanni, On torsion groups with nilpotent automorphism groups, Comm. Algebra 14 (1986), no. 10, 1909–1935. MR 864563, DOI 10.1080/00927878608823402
- László Fuchs, Infinite abelian groups. Vol. I, Pure and Applied Mathematics, Vol. 36, Academic Press, New York-London, 1970. MR 0255673
- Federico Menegazzo and Stewart E. Stonehewer, On the automorphism group of a nilpotent $p$-group, J. London Math. Soc. (2) 31 (1985), no. 2, 272–276. MR 809948, DOI 10.1112/jlms/s2-31.2.272
- Martin R. Pettet, Central automorphisms of periodic groups, Arch. Math. (Basel) 51 (1988), no. 1, 20–33. MR 954064, DOI 10.1007/BF01194150
- D. J. S. Robinson, Applications of cohomology to the theory of groups, Groups—St. Andrews 1981 (St. Andrews, 1981) London Math. Soc. Lecture Note Ser., vol. 71, Cambridge Univ. Press, Cambridge-New York, 1982, pp. 46–80. MR 679154 A. E. Zaleskiĭ, A nilpotent $p$-group has an outer automorphism, Dokl. Akad. Nauk SSSR 196 (1971); Soviet Math. Dokl. 12 (1971), 227-230.
Bibliographic Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 114 (1992), 331-336
- MSC: Primary 20F28; Secondary 20E36
- DOI: https://doi.org/10.1090/S0002-9939-1992-1072334-7
- MathSciNet review: 1072334