Sandwich classification for \(\mathrm{GL}_{n}(R)\), \(\mathrm{O}_{2n}(R)\) and \(\mathrm{U}_{2n}(R,\lambda)\) revisited (Q1693063)

In the theory of linear groups over rings, there is a very important theorem called the sandwich classification theorem (SCT). The SCT for $\mathrm{GL}_n(R)$ was first proved by \textit{H. Bass} in his famous work published in [Publ. Math., Inst. Hautes Étud. Sci. 22, 489--544 (1964; Zbl 0248.18025)]. Later, the SCT became the inspiration for the investigation of many authors in the direction of the description of the lattice of subgroups of linear groups. In the article under review, the author proposed a technique of matrix decomposition due to which he can give new, very short proofs of the sandwich classification theorems for the groups $\mathrm{GL}_n(R)$, $\mathrm O_{2n}(R)$ and $\mathrm U_{2n}(R)$.