Research Projects

The relative autocommuting probability of a finite group G relative to a subgroup H is the probability that an automophism of the group fixes a random element of the subgroup H. This concept, introduced by Gary Sherman in 1975, is crucial for classifying finite groups. This project aims to define and study the set of all relative autocommuting probabilities of a finite group and classify all finite groups in terms of the order of this set. The project is divided into four phases: exploring existing literature, obtaining bounds and computing formulas for relative autocommuting probability, obtaining well-known classes of finite groups, and moving towards classification in terms of the orders of the set of all relative autocommuting probabilities of finite groups. Progress has already been made on characterizations of groups in terms of orders 1, 2, and 3. Dr. Parama Dutta will carry out the research work, taking care of academic and administrative responsibilities such as planning the research problem, working methodology, facility installation, training JRF, and proper utilization of research grants. With over 10 reputed international publications in statistical algebra, the project is confident in achieving the main goal of classification of finite groups in terms of the order of the set of relative autocommuting probabilities. Results from the project may result in publication in reputable journals and national and international collaborations.