Derivations and the permutability of subgroups in polycyclic-by-finite groups
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- by Derek J. S. Robinson PDF
- Proc. Amer. Math. Soc. 130 (2002), 3461-3464 Request permission
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
- Gilbert Baumslag, Frank B. Cannonito, Derek J. Robinson, and Dan Segal, The algorithmic theory of polycyclic-by-finite groups, J. Algebra 142 (1991), no. 1, 118–149. MR 1125209, DOI 10.1016/0021-8693(91)90221-S
- John C. Lennox and Derek J. S. Robinson, Soluble products of nilpotent groups, Rend. Sem. Mat. Univ. Padova 62 (1980), 261–280. MR 582956
- John C. Lennox and John S. Wilson, A note on permutable subgroups, Arch. Math. (Basel) 28 (1977), no. 2, 113–116. MR 491965, DOI 10.1007/BF01223899
- Dan Segal, Decidable properties of polycyclic groups, Proc. London Math. Soc. (3) 61 (1990), no. 3, 497–528. MR 1069513, DOI 10.1112/plms/s3-61.3.497
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
- 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
- © Copyright 2002 American Mathematical Society
- 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
- MathSciNet review: 1918821