On a Generalization of the Hanoi Towers Group

In 2012, Bartholdi, Siegenthaler, and Zalesskii computed the rigid kernel for the only known group for which it is non-trivial, theHanoi towers group. There they determined the kernel was the Klein 4 group. We present a simpler proof of this theorem. In thecourse of the proof, we also compute the rigid stabilizers and present proofs that this group is a self-similar, self-replicating, regular branch group. We then construct a family of groups which generalize the Hanoi towers group and study the congruence subgroup problem for the groups in this family. We show that unlike the Hanoi towers group, the groups in this generalization are just infinite and have trivial rigid kernel. We also put strict bounds on the branch kernel. Additionally, we show that these groups have subgroups of finite index with non-trivial rigid kernel, adding infinitely many new examples. Finally, we show that the topological closures of these groups have Hausdorff dimension arbitrarily close to 1

On (Not) Fearing the Mystery of God (Chapter 8 of The Spirit of Adoption: Writers on Faith, Adoption, God, and More)

Just days before our trip to India, birthplace of my second son, a well-meaning relative cornered me at a family gathering. We\u27ll be praying for you! she said, uttering the Christian phrase that can be, at the same moment, both cliche-riddled and completely sincere. I chose to interpret it as sincere, needing all kinds of prayer for our journey. My husband and I were flying to India with our then six-year-old sons: Benjamin, whom we\u27d adopted from Vietnam as an infant, and Samuel, whom we brought home from Mumbai as a three-year-old. This was no ordinary homeland trip. My adult stepdaughter was marrying an Indian, and we were traveling to her fiance\u27s family village high in the Himalayan foothills for the ceremony