The subgroup determined by a certain ideal in a free group ring

Abstract

For normal subgoups $R$ and $S$ of a free group $F$, an identification of the subgroup $F\cap (1+\mathfrak{rfs})$ is derived, and it is shown that the the quotient $\frac{F\cap (1+\mathfrak{rfs})}{[R^{\prime }\cap S^{\prime },R\cap S][R^{\prime }\cap S,R^{\prime }\cap S][R\cap S^{\prime },R\cap S^{\prime }]}$ is, in general, non-trivial.

7 pages