16 problems

Let $G$ be a compact Lie group, let $BG$ be its classifying space, and let $BP^*(BG)$ denote its Brown–Peterson cohomology ring. Kono–Yagita's nilpotence conjecture. The ring…

Ternary multiplication nilpotence conjecture. The associative algebras $L(A)$ and $R(A)$ are nilpotent; in both cases, the nilpotence is of index $13$ and is not less in general.

7-Engel conjecture. The identity $t_4=0$ implies the $7$-Engel identity.

Symmetric weak nilpotence conjecture. The identity $t_4=0$ does not imply $t_5=0$, and hence does not imply the index-$4$ weak nil property; the identities $t_4=t_5=0$ imply the we…

Nilpotence-index-15 conjecture. The associative algebras $L(A)$ and $R(A)$ are nilpotent; in both cases, the nilpotence is of index $15$ and is not less in general.

Binary weak nilpotence conjecture. For each $n$, the identities $w_n=w_{n+1}=\cdots=w_{2n-3}=0$ imply the identity $w_{2n-2}=0$, and hence imply weak nilpotence of index $n$.

Let $\mathcal{C}$ be a tensor category. For every simple object $L\ne\mathbbm{1}$, require that $\operatorname{Sym} L$ be finite, and for every non-split monomorphism…

Hopkins–Smith vanishing conjecture. The vanishing curve satisfies

Central-commutator nilpotence conjecture. Then

Converse nilpotence conjecture. If

Torsion nilpotence conjecture. Every cohomologically trivial $n$-torsion correspondence $\Gamma$ is nilpotent.

Nilpotence conjecture. If $\Gamma\in \operatorname{End}_{{\mathcal M}_{k,R}}(M)$ is homologically trivial, then there exists an integer $n\gg0$ such that

Let $Q$ be a loop, and let $\operatorname{Inn}(Q)$ denote its inner mapping group. A loop is centrally nilpotent if it has a central series; its nilpotence class is the length of t…

Let $k$ be a commutative ring, let $M$ be an abelian monoid, and let $\mathfrak c=(c_1,c_2,\ldots)$ be a sequence of integers with $c_i\ge 2$. For each $c\ge 2$, the dilation…

Let $p$ be a prime and let $\mathcal{P}^0$ be the endomorphism of $\operatorname{Ext}_P^{*,*}(\mathbb{F}_p,\mathbb{F}_p)$ induced by the $p$th-power map on the polynomial part of t…

Let $p$ be a prime, let $P_*$ be the polynomial part of the dual Steenrod algebra, and let $P$ be its dual. Consider $\operatorname{Ext}_P^{*,*}(\mathbb{F}_p,\mathbb{F}_p)$ and the…