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On the Invariance of a Quotient Group of the Center of F/[R, R]

Published online by Cambridge University Press:  20 November 2018

Trueman MacHenry
Trueman MacHenry*
Affiliation:
Adelphi University, Garden City New York and York University, Toronto
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Let F be a free group of rank ⩾ 2, let F/R ≅ π, and let F0 = F/[R, R]. Auslander and Lyndon showed that the center of Fo is a subgroup of R/[R, R] = Ro, and that it is non-trivial if and only if π is finite [1, corollary 1.3 and theorem 2]. In this paper it will be shown that there is a canonically defined (and not always trivial) quotient group of the center of F which depends only on π.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 5 , October 1969 , pp. 653 - 660
Copyright
Copyright © Canadian Mathematical Society 1969

References

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