Finite \(p\)-groups that determine \(p\)-nilpotency locally

Th. Weigel

A finite \(p\)-group \(P\) is said to determine \(p\)-nilpotency locally if, whenever \(P\) is isomorphic to a Sylow \(p\)-subgroup \(Q\) of a finite group \(G\) and \(N_G(Q)\) is \(p\)-nilpotent, then \(G\) itself is \(p\)-nilpotent. The first examples of finite \(p\)-groups of this type were studied by J. Thévenaz and by H-W. Henn and S. Priddy some time ago. In the talk, we will introduce and discuss a class of finite \(p\)-groups with this property - the class of slim \(p\)-groups.