Topic: What’s Profinite Group?
Speaker: Dy Outdom
Date & Time: Wednesday, 17 June 2026, 10.00–11.00 a.m.
Venue: Room 501, Undergraduate Building, Department of Mathematics, Universitas Gadjah Mada
The Algebra Laboratory held its Weekly Algebra Student Seminar featuring Dy Outdom, who delivered a talk entitled “What’s Profinite Group?”. The seminar introduced participants to the theory of profinite groups, an important area connecting algebra, topology, and number theory.
The presentation began with the notion of topological groups and the construction of inverse limits of topological groups. He explained how inverse systems and their universal properties provide a natural framework for constructing infinite algebraic objects from compatible families of finite groups.
After introducing inverse limits, he focused on the definition and fundamental properties of profinite groups. A profinite group was presented as a topological group that can be realized as the inverse limit of finite groups equipped with the discrete topology. He highlighted important characterizations of profinite groups, including their compactness, Hausdorff property, and total disconnectedness.
The seminar concluded with a brief discussion of further directions, particularly the role of profinite groups in Iwasawa theory and the construction of Iwasawa algebras, which arise as completed group rings associated with profinite groups. These topics form part of the Outdom’s current research interests and highlight the broad applications of profinite methods in contemporary mathematics.
The seminar provided participants with an accessible introduction to profinite groups and demonstrated how inverse limit constructions connect finite algebraic structures with deep problems in number theory and arithmetic geometry.