no. 1
The word problem in polycyclic groups is elementary
Compositio Mathematica, Tome 27 (1973) no. 1, pp. 39-45. 
@article{CM_1973__27_1_39_0,
     author = {Cannonito, F. B. and Gatterdam, R. W.},
     title = {The word problem in polycyclic groups is elementary},
     journal = {Compositio Mathematica},
     pages = {39--45},
     publisher = {Noordhoff International Publishing},
     volume = {27},
     number = {1},
     year = {1973},
     mrnumber = {347990},
     zbl = {0279.20028},
     language = {en},
     url = {http://www.numdam.org/item/CM_1973__27_1_39_0/}
}
TY  - JOUR
AU  - Cannonito, F. B.
AU  - Gatterdam, R. W.
TI  - The word problem in polycyclic groups is elementary
JO  - Compositio Mathematica
PY  - 1973
SP  - 39
EP  - 45
VL  - 27
IS  - 1
PB  - Noordhoff International Publishing
UR  - http://www.numdam.org/item/CM_1973__27_1_39_0/
LA  - en
ID  - CM_1973__27_1_39_0
ER  - 
%0 Journal Article
%A Cannonito, F. B.
%A Gatterdam, R. W.
%T The word problem in polycyclic groups is elementary
%J Compositio Mathematica
%D 1973
%P 39-45
%V 27
%N 1
%I Noordhoff International Publishing
%U http://www.numdam.org/item/CM_1973__27_1_39_0/
%G en
%F CM_1973__27_1_39_0
Cannonito, F. B.; Gatterdam, R. W. The word problem in polycyclic groups is elementary. Compositio Mathematica, Tome 27 (1973) no. 1, pp. 39-45. http://www.numdam.org/item/CM_1973__27_1_39_0/

[1] L. Auslander: On a problem of Phillip Hall. Annals of Math., 86 (1967), 112-116. | MR | Zbl

[2] W.W. Boone: Word problems and recursively enumerable degrees of unsolvability. Annals of Math., 83 (1966), 520-591. | MR | Zbl

[3] W.W. Boone: Word problems and recursively enumerable degrees of unsolvability. A sequel on finitely presented groups. Annals of Math., 84 (1966), 49-84. | MR | Zbl

[4] F.B. Cannonito: Hierarchies of computable groups and the word problem. J. Symbolic Logic, 31 (1966), 376-392. | MR | Zbl

[5] F.B. Cannonito and R.W. Gatterdam: The computability of group constructions, Part I. Word Problems, Boone, Cannonito, Lyndon eds., North-Holland Publishing Company, Amsterdam (1973). | MR

[6] F.B. Cannonito and R.W. Gatterdam: The word problem and power problem in 1-relator groups is primitive recursive (submitted for publication). | Zbl

[7] C.R.J. Clapham: Finitely presented groups with word problem of arbitrary degree of insolubility. Proc. London Math. Soc., 14 (1964), 633-676. | MR | Zbl

[8] R.W. Gatterdam: Embeddings of primitive recursive computable groups (submitted for publication).

[9] R.W. Gatterdam: The computability of group constructions, Part II Bull. Australian Math. Soc., 8 (1973) 27-60. | MR | Zbl

[10] S.C. Kleene: Introduction to Metamathematics. Van Nostrand, Princeton, New Jersey (1952). | MR | Zbl

[11] S. Maclane: Homology. Springer-Verlag, Berlin (1963). | MR | Zbl