TY - JOUR ID - 365 TI - On the nilpotency class of the automorphism group of some finite p-groups JO - Bulletin of the Iranian Mathematical Society JA - BIMS LA - en SN - 1017-060X AU - Fouladi, S. AU - Orfi, R. AD - Y1 - 2011 PY - 2011 VL - 37 IS - No. 3 SP - 281 EP - 289 KW - Finite p-group KW - automorphism group KW - nilpotency class DO - N2 - Let $G$ be a $p$-group of order $p^n$ and $Phi$=$Phi(G)$ be the Frattini subgroup of $G$. It is shown that the nilpotency class of $Autf(G)$, the group of all automorphisms of $G$ centralizing $G/ Fr(G)$, takes the maximum value $n-2$ if and only if $G$ is of maximal class. We also determine the nilpotency class of $Autf(G)$ when $G$ is a finite abelian $p$-group. UR - http://bims.iranjournals.ir/article_365.html L1 - http://bims.iranjournals.ir/article_365_cf69e5755ef787ecc4678fb8887eef0b.pdf ER -