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Derivations and the permutability of subgroups in polycyclic-by-finite groups


Author: Derek J. S. Robinson
Journal: Proc. Amer. Math. Soc. 130 (2002), 3461-3464
MSC (2000): Primary 20F10, 20F16
DOI: https://doi.org/10.1090/S0002-9939-02-06486-9
Published electronically: April 22, 2002
MathSciNet review: 1918821
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Abstract: It is shown that there is an algorithm to decide if two given subgroups of a polycyclic-by-finite group permute. This is accomplished by finding an algorithm which is able to determine if a derivation is surjective.


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

  • 1. G. Baumslag, F. B. Cannonito, D. J. S. Robinson and D. Segal, The algorithmic theory of polycyclic-by-finite groups, J. Algebra 142 (1991), 118-149. MR 92i:20036
  • 2. J. C. Lennox and D. J. S. Robinson, Soluble products of nilpotent groups, Rend. Sem. Mat. Univ. Padova 62 (1980), 261-280. MR 81j:20050
  • 3. J. C. Lennox and J. S. Wilson, A note on permutable subgroups, Arch. Math. (Basel) 28 (1977), 113-116. MR 58:11135
  • 4. D. Segal, Decidable properties of polycyclic groups, Proc. London Math. Soc. (3) 61 (1990), 497-528. MR 91h:20050

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Additional Information

Derek J. S. Robinson
Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, Illinois 61801
Email: robinson@math.uiuc.edu

DOI: https://doi.org/10.1090/S0002-9939-02-06486-9
Received by editor(s): May 29, 2001
Received by editor(s) in revised form: July 5, 2001
Published electronically: April 22, 2002
Communicated by: Steven D. Smith
Article copyright: © Copyright 2002 American Mathematical Society

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