On equality of central and class preserving automorphisms of finite p-groups
Let G be a finite non-abelian p-group, where p is a prime. Let Autc(G) and Autz(G) respectively denote the group of all class preserving and central automorphisms of G. We give a necessary and sufficient condition for G such that Autc(G) = Autz(G) and classify all finite non-abelian p-groups G with elementary abelian or cyclic center such that Autc(G) = Autz(G). We also characterize all finite p-groups G of order ≤ p7 such that Autz(G) = Autz(G) and complete the classification of all finite p-groups of order ≤ p5 for which there exist non-inner class preserving automorphisms.
Key wordsClass preserving automorphism central automorphism camina pair
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