Alladi Ramakrishnan Hall

On boolean interval of finite groups

Sabastien Palcoux and Mamta Balodi

IMSc

Part 1
Speaker: Sebastien Palcoux
Abstract: We will prove a dual version of Ore's theorem for boolean
interval of finite groups having a non-zero Euler characteristic. As a
corollary, we get the result in the group-complemented case using the
usual Ore's theorem. As an application, we get a non-trivial
upper-bound (better than in my previous paper) for the minimal number
of irreducible complex representations generating the left regular
representation of a finite group.

Part 2
Speaker: Mamta Balodi
Abstract: We will first see that the Euler characteristic of an
interval of finite group is the Mobius invariant of its cosets poset
P. Next, in the boolean group-complemented case, we will prove that P
is Cohen-Macaulay, by using the existence of an explicit EL-labeling.
We will then see that the non-trivial Betti number of the order
complex of P is non-zero, by giving an explicit formula.