On the wildness of the description problem for some classes of groups (Q2730539)

The authors show that if \(M_m\) is the direct product of \(m\) copies of a cyclic group of order \(p^s\), \(H\) is a cyclic group of order \(p^n\), \(s\) and \(n\) are arbitrary positive integers different from \(1\), then the description problem for the non-isomorphic extensions of the group \(M_m\) (for an arbitrary positive integer \(m\)) by means of the group \(H\) is wild. It is also shown that the problem of description up to conjugation of finite \(p\)-subgroups of the group \(\text{GL}(n,K)\) for some \(n\) is wild, where \(K\) is the ring of integers or the ring of \(p\)-adic integers.