31/10 -- 16h00 - 16h50
Block Theory for profinite groups (Auditório 208 - Pavilhão de Auditórios)
John William MacQuarrie (UFMG)
Block Theory for finite groups is an approach to the representation theory of finite groups: it starts from the simple observation that the group algebra can be written as a direct product of indecomposable algebras, and it’s enough to study the modules for each factor separately. A profinite group is a (probably infinite) topological group that can be well-understood in terms of its finite quotients. Many facts about finite groups have “profinite analogues”. In this talk, I’ll explain these things and discuss the block theory of profinite groups, arriving at the observation that the finite/profinite analogy in block theory seems to be even stronger than usual!
31/10 -- 16h50 - 17h40
Generalizations of a theorem of Weiss (Auditório 208 - Pavilhão de Auditórios)
Marlon Stefano Fernandes Estanislau (UFMG)
31/10 -- 17h40 - 18h30
Commutative transitive profinite groups (Auditório 208 - Pavilhão de Auditórios)
Luís Augusto de Mendonça (UFMG)
A group G is commutative transitive (CT) if commutativity is a transitive relation for non-trivial elements, that is, if x commutes with both y and z, then y and z commute too. We will discuss the classification of p-adic analytic CT groups and a construction to produce virtually abelian profinite CT groups with a given finite quotient. Joint work with Thomas Weigel (Milano) and Theo Zapata (Brasília).