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Faithful linear representations of certain free nilpotent groups

Published online by Cambridge University Press:  18 May 2009

B. A. F. Wehrfritz
B. A. F. Wehrfritz
Affiliation:
School of Mathematical Sciences, Queen Mary and Westfield College, Mile End Road, London El 4NS, England
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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.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 37 , Issue 1 , January 1995 , pp. 33 - 36
Copyright
Copyright © Glasgow Mathematical Journal Trust 1995

References

REFERENCES

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