## Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

## If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

# Primitive Elements in Free Groups

Martin J. Evans
Proceedings of the American Mathematical Society
Vol. 106, No. 2 (Jun., 1989), pp. 313-316
DOI: 10.2307/2048805
Stable URL: http://www.jstor.org/stable/2048805
Page Count: 4
Let Fn denote the free group of rank n generated by x1, x2,..., xn. We say that y ∈ Fn is a primitive element of Fn if it is contained in a set of free generators of Fn. In this note we construct, for each integer n ≥ 4, an (n - 1)-generator group H that has an n-generator, 2-relator presentation $H = \langlex_1,\ldots, x_n\midr_1, r_2\rangle$ such that the normal closure of $\{r_1, r_2 \}$ in Fn does not contain a primitive element of Fn.