4 problems

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The freeness conjecture for maximal subgroups of free idempotent-generated semigroups
Freeness conjecture. Every maximal subgroup of $\operatorname{IG}(\mathcal{E})$ is a free group.
Conjecturerefutedfree-groups idempotent-generated-semigroups semigroupsarXiv posted 2 days ago
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The conjecture that maximal subgroups of free idempotent-generated semigroups are free
A free idempotent-generated semigroup is an idempotent-generated semigroup determined by an abstract biordered set of idempotents, and its maximal subgroups are the maximal subgrou…
Conjectureopenidempotent-generated-semigroups semigroup-theoryarXiv posted 2 days ago
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The low-rank maximal subgroup conjecture for free idempotent generated semigroups
Low-rank maximal subgroup conjecture. Based on experimental evidence, the maximal subgroup of $IG(E)$ with identity $e$ is $GL_k(Q)$ , at least if $k<n/2$ and $n\geq 3$ .
Conjectureopenidempotent-generated-semigroups linear-groups semigroup-theoryarXiv posted 2 days ago
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The freeness conjecture for maximal subgroups of free idempotent generated semigroups
Freeness conjecture. These maximal subgroups should be free groups.
Conjectureopenfree-groups idempotent-generated-semigroups semigroup-theoryarXiv posted 2 days ago

The freeness conjecture for maximal subgroups of free idempotent-generated semigroups