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Citation Information: Journal of Group Theory. Volume 9, Issue 2, Pages 231–250, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883, DOI: 10.1515/JGT.2006.016, May 2006
This paper deals with an old problem: are there non-trivial finite p-groups which are isomorphic to their full automorphism group, besides the dihedral group of order 8? The answer (in the negative) is obtained in some special cases, including groups of class 2, powerful groups, groups with centre of prime order or an abelian subgroup of prime index, class-3 groups with cyclic centre, groups with coclass at most 3 and others.
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