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Title: Automorphism group of nonabelian groups of order p{sup 3}

Let G be a nonabelian group of order p{sup 3}, 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 p{sup 2}. 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 Z{sub p}, the field of integers modulo p. In this paper, we consider to apply these properties of G to characterize the automorphism group of G.
Authors:
 [1] ;  [2]
  1. Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru (Malaysia)
  2. Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Malaysia and Islamic Azad University-Ahvaz Branch, Ahvaz (Iran, Islamic Republic of)
Publication Date:
OSTI Identifier:
22311400
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 1602; Journal Issue: 1; Conference: 3. international conference on mathematical sciences, Kuala Lumpur (Malaysia), 17-19 Dec 2013; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMMUTATORS; GROUP THEORY; MATHEMATICAL SOLUTIONS; SPACE; VECTORS