|Support type:||Scholarships in Brazil - Post-Doctorate|
|Effective date (Start):||October 01, 2015|
|Effective date (End):||December 18, 2018|
|Field of knowledge:||Physical Sciences and Mathematics - Mathematics - Algebra|
|Principal Investigator:||Mikhailo Dokuchaev|
|Home Institution:||Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil|
|Associated research grant:||15/09162-9 - Non commutative algebra and applications, AP.TEM|
The research project we propose is divided into two parts, the first being the description of possible directions to continue the candidate's PhD research on the subject of the exponent of the Schur multiplier, the latter being the connection with the theory of partial actions via the notion of partial Schur multiplier.The Schur multiplier relates the theory of finite groups with other fields of mathematics, such as algebraic topology. Despite the fact the Schur multiplier is a very classical object, there are many features of it which still remain unclear. Among those, the problem of bounding the exponent of the multiplier in terms of the arithmetical properties of a group continues to attract extensive investigation. The candidate has contributed to this problem introducing the concept of unitary cover. This has been a very successful tool to improve the previously known bounds, and still it shows unhexausted potential. Some of the achieved results are presented hereby in order to introduce new problems.With respect to the theory of partial actions we shall study questions on the partial Schur multiplier, as well as related problems on cohomology of partial actions. Furthermore, partial crossed products and partial group rings shall be also discussed. In particular, we shall try to refine our knowledge on the structure of the components of the partial Schur multiplier, consider projective and injective objects in the category of partial actions, and categorical questions, as well as make efforts on the isomorphism problem for partial group rings.