导群“较小”的极小非p交换p群的分类

Classification of Minimal Non-P-abelian P-groups with Smaller Commutator Subgroup

若群G本身非p交换,但其所有真子群和真商群都p交换,则称群G为极小非p交换p群.设δ(G)为群G的p导群,则有|G':δ(G)|≥p.本文给出了|G':δ(G)|=p的极小非p交换p群的分类.

A finite p- group G is called a minimal non-p- abelian p- groups,if G is not p- abelian and all proper sections of G are p-abelian. Let δ（ G） be p-commutator subgroup of a p-group G,then ｜ G＇： δ（ G） ｜ ≥ p.The minimal non-p-abelian p-groups with ｜ G＇： δ（ G） ｜ = p is given.