25 problems

Let $G$ be an infinite simple tame $K^*$-group, where a $K^*$-group is a group of finite Morley rank in which every proper definable subgroup is a $K$-group, and a $K$-group is one…

Let $\mathfrak{g}$ be an infinite simple Lie ring of finite Morley rank, and suppose that its characteristic is sufficiently large. Cherlin–Zilber conjecture for Lie rings. Then…

A definable simple Lie ring of finite Morley rank is a Lie ring $\mathfrak{g}$ definable in a structure of finite Morley rank. Its characteristic is the characteristic associated w…

Let $n$ be a positive integer, let $H$ be a nonsolvable connected group of finite Morley rank, and suppose that $\operatorname{Alt}(n)$ acts definably and faithfully on $H$ by auto…

Let $(G,X)$ be a connected primitive permutation group of finite Morley rank. Generic transitivity conjecture. Almost all such groups have maximum degree of generic transitivity at…

Super tight programme conjecture. The group $G$ is isomorphic to a Chevalley group $X(K)$ over an algebraically closed field $K$ of characteristic different from $2$.

Let $\mathfrak{g}$ be an infinite simple Lie ring of finite Morley rank. Assume that its characteristic is sufficiently large. Large-characteristic conjecture. Then $\mathfrak{g}$…

Let $(G,S)$ be a definably primitive permutation group of finite Morley rank. Let $b(G,S)$ be the minimal cardinality of a base, and let $b^1(G,S)$ be the least positive integer…

Let $(C < G)$ be a definable, connected, quasi-Frobenius pair of finite Morley rank. Suppose that $G$ is $U_2^\perp$ with involutions, and that the configuration is dihedral. The…

Let $C<G$ be a ranked Frobenius group, where a Frobenius group has a proper subgroup $C$ that is its Frobenius complement. Burdges–Nesin conjecture. The group $G$ is split: there i…

Borovik–Cherlin's projective linearity conjecture. The pair $(G,\Omega)$ is equivalent to

Borovik–Cherlin's conjecture. The group $V$ has the structure of an $n$-dimensional vector space over an algebraically closed field $F$ of Morley rank $1$, and

Finite Morley rank Glauberman conjecture. The group $G$ is solvable.

Let $G$ be an infinite simple group of finite Morley rank, and let $\alpha$ be a generic automorphism of $G$. The fixed-point subgroup of $\alpha$ is $C_G(\alpha)$. Principal conje…

Let $(G,V)$ be a faithful, irreducible module of finite Morley rank, where $G=\mathbb{G}(\mathbb{K})$ is the group of $\mathbb{K}$-points of a simple algebraic group. Definable twi…

Let $G$ be a simple group of finite Morley rank definable in a Zariski geometry. Zariski-geometry algebraicity conjecture. The group $G$ has a Lie algebra and is a simple algebraic…

Let $(G,V)$ be a faithful, irreducible module of finite Morley rank, with $G$ connected. A pseudoreflection subgroup is an abelian subgroup $R$ such that … and $R$ acts transitivel…

Let $(G,V)$ be a faithful module of finite Morley rank, and suppose that $V$ has Morley rank $n$ and $G$ is generically $n$-transitive. Highly generically transitive module conject…

Let $(G,V)$ be a module of finite Morley rank, with $G$ connected and simple modulo its at most finite centre. Suppose that $G$ is transitive on $V\setminus\{0\}$ and generically…

Let $G$ be a simple group of finite Morley rank admitting a generically $4$-transitive action. Generically 4-transitive classification conjecture. Either…

Let $G$ be a connected group of finite Morley rank acting faithfully, definably and transitively on a set $X$ of Morley rank $n$, and suppose the action is generically $(n+2)$-tran…

Let $(G,X)$ be a faithful definable permutation group of finite Morley rank, let $G$ be connected and definably primitive on $X$, and let $b(G)$ denote the minimal cardinality of a…

Let $G$ be a simple group of finite Morley rank. The algebraicity conjecture. $G$ is an algebraic group. This is presented as a long-standing open classification problem in model t…

Recognition conjecture. If $(X,G)$ is transitive and generically $(n+2)$-transitive, then $(X,G)$ is equivalent to

Genericity Conjecture. The union of the connected definable nilpotent subgroups of $G$ contains a definable generic subset of $G$.