On isomorphism of Sylow subgroups of the general linear group over the ring of integers (Q1592187)

Let \(\mathbb{Z}\) be the ring of integers and \(n\) a positive integer. The authors investigate the isomorphism problem for Sylow subgroups of \(\text{GL}(n,\mathbb{Z})\), and deduce a necessary and sufficient condition for all Sylow \(p\)-subgroups of \(\text{GL}(n,\mathbb{Z})\) (\(n\geq 2\)) to be pairwise isomorphic. The same problem over the ring \(\mathbb{Z}_q\) of \(q\)-adic integers is also solved.