Groups of prime-power order with a small second derived quotient

الأصل · EN

For odd primes we prove some structure theorems for finite p-groups G, such that G''≠ 1 and |G'/G''|=p³. Building on results of Blackburn and Hall, it is shown that G3 is a maximal subgroup of G', the group G has a central decomposition into two simpler subgroups, and, moreover, G' has one of two isomorphism types.