Formal Conjectures is a Lean 4 benchmark containing 2615 formalized problems with 1029 open conjectures, designed to evaluate automated mathematical reasoning and proof discovery.
Unsolved Problems in Group Theory. The Kourovka Notebook
6 Pith papers cite this work. Polarity classification is still indexing.
6
Pith papers citing it
abstract
This is a collection of open problems in group theory proposed by hundreds of mathematicians from all over the world. It has been published every 2--4 years since 1965. This is the 21st edition, which contains 150 new problems and a number of comments on problems from the previous editions.
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Every group embeds malnormally into a simple complete co-Hopfian group, so non-trivial endomorphisms extend to the larger group if and only if they are inner automorphisms.
Finite LCM-groups of equal order have equal sum of element orders precisely when they have the same order type.
3-manifold groups, limit groups, and selected one-relator and right-angled Artin groups possess the local lifting property and property FD, implying flexible stability of their approximate representations.
The recognition problem by element orders is solved for every finite simple linear and unitary group.
Proves K4 exists in derangement graphs of transitive groups with degree >30, implying |G:U|≤10 for normal G in A with |A:G|=3 under union-of-conjugates condition, supporting Neumann-Praeger conjecture.
citing papers explorer
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Formal Conjectures: An Open and Evolving Benchmark for Verified Discovery in Mathematics
Formal Conjectures is a Lean 4 benchmark containing 2615 formalized problems with 1029 open conjectures, designed to evaluate automated mathematical reasoning and proof discovery.
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An improved characterisation of inner automorphisms of groups
Every group embeds malnormally into a simple complete co-Hopfian group, so non-trivial endomorphisms extend to the larger group if and only if they are inner automorphisms.
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On the Sum of Element Orders in Finite Abelian Groups
Finite LCM-groups of equal order have equal sum of element orders precisely when they have the same order type.
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The Local Lifting Property, Property FD, and stability of approximate representations
3-manifold groups, limit groups, and selected one-relator and right-angled Artin groups possess the local lifting property and property FD, implying flexible stability of their approximate representations.
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Recognition by element orders for simple linear and unitary groups
The recognition problem by element orders is solved for every finite simple linear and unitary group.
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Kronecker classes and cliques in derangement graphs
Proves K4 exists in derangement graphs of transitive groups with degree >30, implying |G:U|≤10 for normal G in A with |A:G|=3 under union-of-conjugates condition, supporting Neumann-Praeger conjecture.