Sarmin, Nor Haniza and Barakat, Yasamin (2014) Automorphism group of nonabelian groups of order p3. AIP Conference Proceedings, 1602 . pp. 640-643. ISSN 0094-243X
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Official URL: http://dx.doi.org/10.1063/1.4882552
Abstract
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.
Item Type: | Article |
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Uncontrolled Keywords: | automorphism, nilpotency of class 2, p-group, two generated |
Subjects: | Q Science > QA Mathematics |
Divisions: | Science |
ID Code: | 51970 |
Deposited By: | Siti Nor Hashidah Zakaria |
Deposited On: | 01 Feb 2016 03:53 |
Last Modified: | 30 Nov 2018 06:57 |
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