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2009•MathematikaRequires access

Presentation of 2-Group of Order 32

Abdullah Tahir Othman, Sharmila Karim

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Abstract

Research on the presentation of 2-groups of order $2^n,$ $(n\le 6)$ was founded by Hall et al. [4] and was continued by Sag et al [7]. This paper focuses on the presentation of 2-groups of order $2^5$ where there are 51 groups comprising of 7 Abelian groups and 44 non-Abelian groups. We are more concerned in finding the structures for each of the every 44 non-Abelian groups to show that these groups are not isomorphic to each other using GAP (Groups, Algorithms, and Programming) software. Keywords: 2-Group; group presentation; isomorphism; non-Abelian group.

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What this paper is about

Research on the presentation of 2-groups of order $2^n,$ $(n\le 6)$ was founded by Hall et al. [4] and was continued by Sag et al [7]. This paper focuses on the presentation of 2-groups of order $2^5$ where there are 51 groups comprising of 7 Abelian groups and 44 non-Abelian groups. We are more concerned in finding the structures for each of the every 44 non-Abelian groups to show that these groups are not isomorphic to each other using GAP (Groups, Algorithms, and Programming) software. Keywords: 2-Group; group presentation; isomorphism; non-Abelian group.

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Available abstract

Research on the presentation of 2-groups of order $2^n,$ $(n\le 6)$ was founded by Hall et al. [4] and was continued by Sag et al [7]. This paper focuses on the presentation of 2-groups of order $2^5$ where there are 51 groups comprising of 7 Abelian groups and 44 non-Abelian groups. We are more concerned in finding the structures for each of the every 44 non-Abelian groups to show that these groups are not isomorphic to each other using GAP (Groups, Algorithms, and Programming) software. Keywords: 2-Group; group presentation; isomorphism; non-Abelian group.

Key concepts: Abelian group, Mathematics, Elementary abelian group, Presentation (obstetrics), Group (periodic table), G-module, Order (exchange), Non-abelian group

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