SEMINAR: Groups and Combinatorics Seminar: UCS groups and associated algebras

Time and place: 3pm Friday 20 March in Blakers LT.

Speaker: Frederico A. M. Ribeiro (Federal University of Minas Gerais)

Title: UCS groups and associated algebras.

Abstract: Groups having many characteristic subgroups tend to have simpler automorphism subgroups, so it might be a good idea to look into the automorphism subgroups of groups having few characteristic subgroups. While characteristically simple groups are well understood, this is not the case when "few" is greater than zero. UCS groups are groups having a unique non-obvious characteristic subgroup. When investigating one of the two classes of UCS p-groups, I, together with Csaba Schneider, showed that they could be associated bijectively with a class of algebras we called IAC (irreducible and anticommutative). We can then, by looking into properties of these algebras, gather information about the groups.