Research on algebraic structures related to subgroup families of finite groups

2016 Fiscal Year Final Research Report

• Project/Area Number: 25400006
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Chiba University
• Principal Investigator: Sawabe Masato 千葉大学, 教育学部, 准教授 (60346624)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Keywords: 有限群 / 単体複体

Outline of Final Research Achievements

We regard a subgroup complex as a quiver. Then, by using the associated path algebra and its representation, we provide a new method for studying finite groups via subgroup complexes. Indeed, we introduce an integer called a generating constant from representations of path algebra, and applying those constants, we characterize finite solvable groups. In addition to this, we prove new properties of complex irreducible characters of finite groups. For further development on this research in the future, we focus on nilpotent subgroup complexes, and establish fundamental theory on homotopy and homology of such complexes.

Free Research Field

有限群