Let G be a group. An automorphism of G is called intense if it
sends each subgroup of G to a conjugate; the collection of such
automorphisms is denoted by Int(G). In the special case in which p
is a prime number and G is a finite p-group, one can show that
Int(G) is the semidirect product of a normal p-Sylow and a cyclic
subgroup of order dividing p?1. In this paper we classify the
finite p-groups whose groups of intense automorphisms are not
themselves p-groups. It emerges from our investigation that the
structure of such groups is almost completely determined by their
nilpotency class: for p > 3, they share a quotient, growing with
their class, with a uniquely determined infinite 2-generated pro-p
group.
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