Index Sets of some Computable Groups

1 Acknowledgements I would first like to thank my advisor Professor Karen Lange. She has quite literally taught me everything I know about computability. She has helped me develop as not only a math researcher, but also a writer and presenter. I would also like to thank NSF grant DMS-1100604 for funding summer research that was instrumental in helping me complete this thesis. I would also like to thank my entire thesis committee, Professor Diesl and Professor Shuchat of the math department and Professor McGowan of the philosophy department. Special thanks to Professor Diesl for meeting with me multiple times this semester to discuss my thesis research. In addition, I would like to thank all of my professors in the Wellesley math department for sharing with me their knowledge and passion for math. I also have to thank all of my amazing friends in the math department for their constant support throughout this process, and for the past four years. Together we have made it through seemingly endless problem sets and our transitions to the world of math research. Finally, I would like to thank all of my friends and family who have shaped my time here at Wellesley. Thanks to my father who first inspired my love of math, and my mother and sister who have consistently supported me and put up with all of my math talk. Thanks to all of my amazing Wellesley friends without whom my time at Wellesley would be unrecognizable.