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We apply these results to a number of examples, including the self-similar group actions associated to integer dilation matrices, and the canonical self-similar actions of the basilica group and the Grigorchuk group.
We denote by (mathfrak{B }) the Basilica group.
(Erschler) Any finitely presented cover of the Basilica group (mathfrak{B }) has non-abelian free subgroups.
The other uses the contracting property of the Basilica group established in [80] and follows the idea indicated in [66] for (mathfrak{G }).
(iv) The Basilica group (mathfrak{B }) is just non-soluble, which means that all its proper quotients are soluble [80, Proposition 6].
The class (mathcal{AG }backslash mathcal{SG }) contains the Basilica group(mathfrak{B }) of Example 2.17, which was first shown to be not in (mathcal{SG }) [80], and later shown to be amenable [10].
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For the Basilica automaton, the group (G^* A, tau )) coincides with (mathfrak{B }), and Theorem 1.8 follows.
Miguel Ángel Trejo Sardoa, 66, admired the basilica with a group of friends after attending the morning Mass, held daily.
Just outside the basilica, I watched a group of men working in a cordoned-off area, carefully digging and brushing dirt and dust off a mosaic floor.
On Friday, the group finally left the basilica, venerated by many Christians as the birthplace of Jesus.
If you secretly tag along with a tour group, you can slip into the Basilica from the Sistine Chapel without having to queue again.
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