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Let $G$ denote the projective special linear group $\text{PSL}(2,q)$, for aprime power $q$. It is shown that a finite 2-subgroup of the group$V(\mathbb{Z}G)$ of augmentation 1 units in the integral group ring$\mathbb{Z}G$ of $G$ is isomorphic to a subgroup of $G$. Furthermore, it isshown that a composition factor of a finite subgroup of $V(\mathbb{Z}G)$ isisomorphic to a subgroup of $G$.

Finite groups of units and their composition factors in the integral group rings of the groups $\text{PSL}(2,q)$