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Derivations and the permutability of subgroups in polycyclic-by-finite groups
Author(s):
Derek
J. S.
Robinson
Journal:
Proc. Amer. Math. Soc.
130
(2002),
3461-3464.
MSC (2000):
Primary 20F10, 20F16
Posted:
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:
-
- 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:
10.1090/S0002-9939-02-06486-9
PII:
S 0002-9939(02)06486-9
Received by editor(s):
May 29, 2001
Received by editor(s) in revised form:
July 5, 2001
Posted:
April 22, 2002
Communicated by:
Steven D. Smith
Copyright of article:
Copyright
2002,
American Mathematical Society
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