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The Sylow $ p$-subgroups of semicomplete nilpotent groups


Authors: Martyn R. Dixon and E. Myron Rigsby
Journal: Proc. Amer. Math. Soc. 119 (1993), 341-349
MSC: Primary 20F18; Secondary 20D20, 20F28
DOI: https://doi.org/10.1090/S0002-9939-1993-1152977-3
MathSciNet review: 1152977
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Abstract: A nilpotent group whose group of outer automorphisms is trivial may contain elements of finite order. This paper is concerned with how large the Sylow $ p$-subgroups of such a group can be. We show that in many cases the Sylow $ p$-subgroups of such a semicomplete nilpotent group are always finite.


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  • [1] T. A. Fournelle, Outer automorphisms of nilpotent groups, Bull. London Math. Soc. 13 (1981), 129-132. MR 608096 (82d:20037)
  • [2] -, Nilpotent groups without periodic automorphisms, Bull. London Math. Soc. 15 (1983), 590-595. MR 720747 (85b:20050)
  • [3] -, Torsion in semicomplete nilpotent groups, Math. Proc. Cambridge Philos. Soc. 94 (1983), 191-202. MR 715050 (85c:20028)
  • [4] -, Automorphisms of nilpotent groups of class two with small rank, J. Austral. Math. Soc. Ser. A 39 (1985), 121-131. MR 786982 (87a:20038)
  • [5] S. Franciosi and F. deGiovanni, A note on groups with countable automorphism group, Arch. Math. 47 (1986), 12-16. MR 855132 (87i:20066)
  • [6] L. Fuchs, Infinite abelian groups, Academic Press, New York, 1973. MR 0349869 (50:2362)
  • [7] W. Gaschütz, Kohomologische Trivialität und äussere Automorphismen von $ p$-Gruppen, Math. Z. 88 (1965), 432-433. MR 0195941 (33:4137)
  • [8] -, Nichtabelsche $ p$-Gruppen besitzen äussere $ p$-Automorphismen, J. Algebra 4 (1966), 1-2. MR 0193144 (33:1365)
  • [9] H. Heineken, Automorphism groups of torsionfree nilpotent groups of class $ 2$, Sympos. Math. 17 (1976), 235-250. MR 0419627 (54:7645)
  • [10] D. J. S. Robinson, Outer automorphisms of torsionfree nilpotent groups, preprint.
  • [11] -, Finiteness conditions and generalized soluble groups (2 vols.), Springer-Verlag, New York, 1972.
  • [12] -, Infinite torsion groups as automorphism groups, Quart. J. Math. Oxford (2) 30 (1979), 351-364. MR 545070 (81c:20023)
  • [13] R. B. Warfield, Nilpotent groups, Lecture Notes in Math., vol. 513, Springer-Verlag, New York, 1972.
  • [14] A. E. Zalesskiĭ, A nilpotent $ p$-group possesses an outer automorphism, Dokl. Akad. Nauk. SSSR 196 (1971), 751-754; English transl., Soviet Math. Dokl. 12 (1971), 227-230. MR 0274587 (43:350)
  • [15] -, An example of a torsionfree nilpotent group having no outer automorphisms, Mat. Zametki 11 (1972), 21-26; English transl., Math. Notes 11 (1972), 16-19. MR 0291291 (45:385)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1993-1152977-3
Keywords: Automorphism, semicomplete nilpotent group
Article copyright: © Copyright 1993 American Mathematical Society

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