# Infinite systolic groups are not torsion

```@article{Prytula2018InfiniteSG,
title={Infinite systolic groups are not torsion},
author={Tomasz Prytula},
journal={Colloquium Mathematicum},
year={2018},
volume={153},
pages={169-194}
}```
• Tomasz Prytula
• Published 2018
• Mathematics
• Colloquium Mathematicum
• We study \$k\$-systolic complexes introduced by T. Januszkiewicz and J. Świątkowski, which are simply connected simplicial complexes of simplicial nonpositive curvature. Using techniques of filling diagrams we prove that for \$k \geq 7\$ the \$1\$-skeleton of a \$k\$-systolic complex is Gromov hyperbolic. We give an elementary proof of the so-called Projection Lemma, which implies contractibility of \$6\$-systolic complexes. We also present a new proof of the fact that an infinite group acting… CONTINUE READING

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