4 problems

For an integer $n\geqslant2$, let $\mathbb{Z}_{\!/2}^n$ denote the direct sum of $n$ copies of the cyclic group $\mathbb{Z}_{\!/2}$. Let $\lambda(\mathbb{Z}_{\!/2}^n)$ denote its L…

Conjectural tensor-product formulae.

For an odd prime $p$, an elementary abelian $p$-group is a group isomorphic to $(\mathbb{Z}/p\mathbb{Z})^r$. Nonexistence conjecture for elementary abelian class groups. No element…

Let $C$ be an elementary abelian $p$-group of rank $c$, and let $\rho$ be a faithful $n$-dimensional complex representation of $C$. Let $e(\rho)$ be the top degree of the indecompo…