On the Vanishing Criterion for the Cohomology Groups of the Automorphism Group of a finite Abelian $p$-Group

Chudamani Pranesachar Anil Kumar, Soham Swadhin Pradhan

For a partition $\underline{\lambda }=({\lambda }_1^{{\rho }_1}>{\lambda }_2^{{\rho }_2}>{\lambda }_3^{{\rho }_3}>\dots >{\lambda }_k^{{\rho }_k})$ and its associated finite abelian $p$-group $\mathcal{A}_{\underlineλ}=\underset{i=1}{\over…