#### 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.

Done