Geodesic
The order problem and the power problem for free product sixth-groups
Glasgow mathematical journal, Tome 10 (1969) no. 1, pp. 1-9

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Let G be a group given in terms of generators and denning relations. The order problem is said to be solvable for (the given presentation of) the group G if, given any element W of G (as a word in the given generators of G), we can determine the order of W in G. The power problem is solvable for G if, given any pair X, Y of elements of G, we can determine whether or not X belongs to the cyclic subgroup {Y} of G generated by Y. It is easy to see that if either of these problems is solvable for G, then the word problem is also solvable for G. 
McCool, James. The order problem and the power problem for free product sixth-groups. Glasgow mathematical journal, Tome 10 (1969) no. 1, pp. 1-9. doi: 10.1017/S0017089500000458
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