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,...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.展开更多
文摘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.
