Department of Mathematics, Shanxi Normal University, Linfen 041004, China
Abstract:
Assume that G is a finite non-Dedekind p-group. D. S. Passman introduced the following concept: we say that H1 < H2 < ? < Hk is a chain of nonnormal subgroups of G if each Hi ? G and if |Hi : Hi?1| = p for i = 2, 3,…, k. k is called the length of the chain. chn(G) denotes the maximum of the lengths of the chains of nonnormal subgroups of G. In this paper, finite 2-groups G with chn(G) ? 2 are completely classified up to isomorphism.