Geodesic
Non-cancellative power-free groups
Glasgow mathematical journal, Tome 7 (1966) no. 4, pp. 207-212

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A. Geddes [1, Theorem 3.3] has shown that the partial algebraic system which he has called a power-free group need not be cancellative. In other words, there exist power-free groups containing at least one element a with the property that ab can equal ac when b ≠ c. In the present paper we propose to study the structure of such non-cancellative power-free groups, and we shall in fact obtain a complete solution to this problem. 
Walker, R. G. Non-cancellative power-free groups. Glasgow mathematical journal, Tome 7 (1966) no. 4, pp. 207-212. doi: 10.1017/S2040618500035449
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[1] 1.Geddes, A., Power-free groups, Proc. Cambridge Philos. Soc. 60 (1964), 393–408. Google Scholar | DOI

[2] 2.Geddes, A. and Walker, R. G., The structure of cancellative power-free groups, Proc. Glasgow Math. Assoc. 7 (1966), 199–206. Google Scholar | DOI

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