Geodesic
On the Invariance of a Quotient Group of the Center of F/[R, R]
Canadian mathematical bulletin, Tome 12 (1969) no. 5, pp. 653-660

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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. 
MacHenry, Trueman. On the Invariance of a Quotient Group of the Center of F/[R, R]. Canadian mathematical bulletin, Tome 12 (1969) no. 5, pp. 653-660. doi: 10.4153/CMB-1969-084-6
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     title = {On the {Invariance} of a {Quotient} {Group} of the {Center} of {F/[R,} {R]}},
     journal = {Canadian mathematical bulletin},
     pages = {653--660},
     year = {1969},
     volume = {12},
     number = {5},
     doi = {10.4153/CMB-1969-084-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1969-084-6/}
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