Automorphism group of nonabelian groups of order p3

• Main Authors: Sarmin, Nor Haniza, Barakat, Yasamin
• Format: Article
• Published: American Institute of Physics Inc. 2014
• Subjects: QA Mathematics
• Online Access: http://eprints.utm.my/id/eprint/51970/; http://dx.doi.org/10.1063/1.4882552

Let G be a nonabelian group of order p3, where p is a prime number. Then G is a two generated group that its commutator, centre and Frattini subgroup coincide and are of order p. Hence, the quotient group of G over its centre and also Frattini quotient group of G, both are of order p2. However, the first mentioned quotient is isomorphic to the inner group of G, which is a normal subgroup of automorphism group of G. Whereas, Frattini quotient group of G is an abelian elementary group that can be considered as a vector space of dimension two over Zp, the field of integers modulo p. In this paper, we consider to apply these properties of G to characterize the automorphism group of G.