A normal subgroup $N$ of a group $G$ is said to be an omissible subgroup of $G$ if it has the following property: whenever $X\leq G$ is such that $G=XN$, then $G=X$. In this note we construct various groups $G$, each of which has an omissible subgroup $N\neq 1$ such that $G/N\cong SL_2(k)$ where $k$ is a field of positive characteristic.

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