Finite 2-groups whose length of chain of nonnormal subgroups is at most 2

摘要

Assume that G is a finite non-Dedekind p -group. D. S. Passman introduced the following concept: we say that H ~(1)< H ~(2)< ⋯ < H ~( k )is a chain of nonnormal subgroups of G if each H ~( i )⋬ G and if | H ~( i ): H ~( i −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.