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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
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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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