no. 1
The word problem in polycyclic groups is elementary
Compositio Mathematica, Tome 27 (1973) no. 1, pp. 39-45 
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     title = {The word problem in polycyclic groups is elementary},
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     pages = {39--45},
     year = {1973},
     publisher = {Noordhoff International Publishing},
     volume = {27},
     number = {1},
     mrnumber = {347990},
     zbl = {0279.20028},
     language = {en},
     url = {https://www.numdam.org/item/CM_1973__27_1_39_0/}
}
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Cannonito, F. B.; Gatterdam, R. W. The word problem in polycyclic groups is elementary. Compositio Mathematica, Tome 27 (1973) no. 1, pp. 39-45. https://www.numdam.org/item/CM_1973__27_1_39_0/

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