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

Journal Article · Thu Jun 19 00:00:00 EDT 2014 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.4882552· OSTI ID:22311400

Sarmin, Nor Haniza ^[1]; Barakat, Yasamin ^[2]

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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)

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.

• OSTI ID: 22311400
• Journal Information: AIP Conference Proceedings, Vol. 1602, 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); ISSN 0094-243X
• Country of Publication: United States
• Language: English

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