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Using a data sample of events collected with the BESIII detector at the BEPCII collider, we present measurements of branching fractions for the decays $\chi_{cJ} \rightarrow \Sigma^+ \bar{\Sigma}^-\Sigma^0 \bar{\Sigma}^0\chi_{c1,2}\rightarrow \Sigma^+ \bar{\Sigma}^-\Sigma^0 \bar{\Sigma}^0\chi_{c0}\rightarrow \Sigma^+ \bar{\Sigma}^-\Sigma^0 \bar{\Sigma}^0$ decays are measured with improved precision. The branching fraction ratios between the charged and neutral modes are consistent with the prediction of isospin symmetry.

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