Geodesic
Faithful linear representations of certain free nilpotent groups
Glasgow mathematical journal, Tome 37 (1995) no. 1, pp. 33-36

Voir la notice de l'article provenant de la source Cambridge University Press

Brian Hartley asked me whether a free (nilpotent of class 2 and exponent p2)-group of countable rank has a faithful linear representation of finite degree, p here being a prime of course. The answer is yes. The point is that this then yields via work of F. Leinen and M. J. Tomkinson, see [3,3.6] an image of a linear p-group, which is not even finitary linear. The question of which relatively free groups have faithful linear representations dates back at least to work of W. Magnus in the 1930's, see [4, pp. 33, 34 and the final comment on p. 40] for a discussion of this. Our construction, which works more generally, is a further contribution. We write Rc for the variety of nilpotent groups of class at most c and (C9 for the variety of groups of exponent dividing q. 
Wehrfritz, B. A. F. Faithful linear representations of certain free nilpotent groups. Glasgow mathematical journal, Tome 37 (1995) no. 1, pp. 33-36. doi: 10.1017/S0017089500030354
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