15 problems

Generalized Benson conjecture. If $(\mathcal{C},G')$ is an induced $p'$-symmetry of $V$, then every prime dividing the order of $G'$ is less than $p$.

Generalized Benson conjecture. Every prime dividing the order of $G'$ is less than $p$.

Benson's conjecture. All indecomposable summands of $V\otimes V^*$ have dimension divisible by $2$, except for the single summand isomorphic to the trivial representation $\Bbbk$;…

Let $p$ be a prime and let $G$ be a finite $p$-group. The Loewy length $\mathsf{L}(G)$ is the nilpotency index of the Jacobson radical of the group algebra $\mathbb{F}_p[G]$, and…

Let $p$ be a prime, let $G$ be a finite $p$-group, and let $K(G,C_p)$ denote the module of relative $(G,C_p)$-Brauer relations. For a sub-quotient $P=K/N$ of $G\times C_p$, write…

Berkovich's conjecture. Every finite nonabelian $p$-group admits a non-inner automorphism of order $p$.

Let $p$ be an odd prime and let $r\geq p-1$ be an integer. Let … be the finite $p$-group defined in the source. Depth-two conjecture. The mod-$p$ cohomology ring…

Let $G$ be a finite $p$-group. Define $\omega_a(G)$ as the minimum of $\dim \operatorname{H}^{*}(G;\mathbb{F}_p)/\mathfrak{p}$ over associated primes $\mathfrak{p}$ of…

Let $G$ be a finite $p$-group, and write $M(G)=H_2(G,\mathbb{Z})$ for its Schur multiplier. Write $\operatorname{exp}(G)$ for the exponent of $G$. Exponent conjecture for finite…

Let $G$ be a powerful $4^*$-central $2$-group with the $\Omega$EP property, and let $d=\operatorname{rk}(\Omega_1(G))$. Write $\Lambda$ for the exterior algebra. The cohomology con…

Let $G$ be a finite $p$-group of fixed rank $r$. A subgroup $K$ is powerful $p^*$-central with the $\Omega$EP if it has those properties. The powerful $p^*$-central subgroup conjec…

Stable-cohomology top-degree conjecture. There exists a $G$-module $A$ with trivial action such that

Let $p$ be a prime, let $k$ be a field of characteristic $p$, and let $(G_i \mid i \geq 0)$ be a coclass family of finite $p$-groups. Cohomology stabilization conjecture. There exi…

Schmid's cohomological conjecture. For every integer $n$, one has

Let $p$ be a prime, let $G$ be a finite $p$-group, and let $H\cong \mathbb Z_p$. Write $\tilde G=G\times H$, let $N(G,H)$ denote the relative Burnside kernel, and for a subquotient…