A p-stable action of the automorphism group of a group (Q1108376)

The author considers a problem concerned with p-stability, where p is some prime. This is an idea which can be found in \textit{D. Gorenstein} [Finite Groups (1968; Zbl 0185.057), 3.8]. Let G be a group and let its automorphism group be Aut(G). This is said to be p-stable over G, if whenever A is a p-subgroup of Aut(G) and B is a p-subgroup of G fixed by A with \([B,A,A]=1\) then \([A,N_{Aut(G)}(B)]<C_{Aut(G)}(B)\). The author then proves the main theorem which says that if Aut(G) is not stable over G then G involves SL(2,p). This is a generalization of a number of earlier results concerning the original concept of p-stability. \{page 2, line 8 ``affin'' should be affine; page 2 line 9 the word ``adequated'' seems odd, page 2 line 2 of Definition 1 ``estable'' should be ``stable''.\}