Ihechukwu Chinyere

Unipotence of a double commutator with transvections

Let $R$ be a nonzero commutative ring with identity, $n\geq3$, and $\sigma\in GL_n(R)$. We prove that there exist nonidentity transvections $\tau_1,\tau_2\in GL_n(R)$ such that $\big[[\sigma,\tau_1],\tau_2\big]=I_n$. Hence, Kourovka Notebook Problem 10.46 has a stronger affirmative answer over commutative rings with id...