Abstract
The main result of this paper shows that if G is a finite nonabelian p -group and if C G ( Z (( G ))) ≠ ( G ), then G has a noninner automorphism of order p which fixes ( G ). This reduces the verification of the longstanding conjecture that every finite nonabelian p -group G has a noninner automorphism of order p to the degenerate case in which C G ( Z (( G ))) = ( G ).
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