We prove that infinitely presented graphical G r ( 7 ) small cancellation groups are acylindrically hyperbolic. In particular, infinitely presented classical C ( 7 ) -groups and, hence, classical C ' ( 1 6 ) -groups are acylindrically hyperbolic. We also prove the analogous statements for the larger class of graphical small cancellation presentations over free products. We construct infinitely presented classical C ' ( 1 6 ) -groups that provide new examples of divergence functions of groups.
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Gruber et al. (2018) studied this question.
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