3 problems

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Elkasapy's nilpotency conjecture for commutator words
Elkasapy's nilpotency conjecture. The lower bound is an equality:
Conjectureopencommutator-width group-theory nilpotent-groupsarXiv posted 2 days ago
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The commutator-width conjecture for traces in $\Gamma(2)'$
Let $\Gamma(2)'$ be the commutator subgroup of $\Gamma(2)$ , and let $\operatorname{Tr}(\Gamma(2)')$ denote its trace set. The commutator width of an element is the minimum number o…
Conjectureopencommutator-width modular-groups trace-formulasarXiv posted 2 days ago
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The conjecture that every element of $\operatorname{SL}_3(\mathbb{Z})$ is a 1-commutator
Let $g\in \operatorname{SL}_3(\mathbb{Z})$ . A 1-commutator is an element expressible as $[x,y]=xyx^{-1}y^{-1}$ for some $x,y\in\operatorname{SL}_3(\mathbb{Z})$ . The 1-commutator co…
Conjectureopencommutator-width linear-groupsarXiv posted 2 days ago

Elkasapy's nilpotency conjecture for commutator words