On Some Problems in Group Theory of Probabilistic Nature
The determination of the abelianness of a nonabelian group has been introduced for symmetric groups by Erdos and Turan in 1968. In 1973, Gustafson did the same for finite groups while MacHale determined the abelianness for finite rings in 1974. Basic probability theory will be used in connection wit...
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my.utm.380112017-03-03T05:49:28Z http://eprints.utm.my/id/eprint/38011/ On Some Problems in Group Theory of Probabilistic Nature Mohd. Ali, Nor Muhainiah Sarmin, Nor Haniza QA Mathematics The determination of the abelianness of a nonabelian group has been introduced for symmetric groups by Erdos and Turan in 1968. In 1973, Gustafson did the same for finite groups while MacHale determined the abelianness for finite rings in 1974. Basic probability theory will be used in connection with group theory. This paper will focus on the 2-generator 2-groups of nilpotency class 2 based on the classification that has been done by Kappe et.al in 1999. In this paper some results on Pn(G), the probability that the nth power of a random element in a group G commutes with another random element from the same group, will be presented. Penerbit Universiti Putra Malaysia, Serdang 2010 Article PeerReviewed text/html en http://eprints.utm.my/id/eprint/38011/2/MM%20v.32%282%292010_35_41.pdf Mohd. Ali, Nor Muhainiah and Sarmin, Nor Haniza (2010) On Some Problems in Group Theory of Probabilistic Nature. Menemui Matematik (Discovering Mathematics), 32 (2). pp. 35-41. ISSN 2231-7023 http://math.upm.edu.my/dismath/paper/2010/MM%20v.32(2)2010_35_41.pdf |
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The determination of the abelianness of a nonabelian group has been introduced for symmetric groups by Erdos and Turan in 1968. In 1973, Gustafson did the same for finite groups while MacHale determined the abelianness for finite rings in 1974. Basic probability theory will be used in connection with group theory. This paper will focus on the 2-generator 2-groups of nilpotency class 2 based on the classification that has been done by Kappe et.al in 1999. In this paper some results on Pn(G), the probability that the nth power of a random element in a group G commutes with another random element from the same group, will be presented. |
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Article |
author |
Mohd. Ali, Nor Muhainiah Sarmin, Nor Haniza |
author_facet |
Mohd. Ali, Nor Muhainiah Sarmin, Nor Haniza |
author_sort |
Mohd. Ali, Nor Muhainiah |
title |
On Some Problems in Group Theory of Probabilistic Nature |
title_short |
On Some Problems in Group Theory of Probabilistic Nature |
title_full |
On Some Problems in Group Theory of Probabilistic Nature |
title_fullStr |
On Some Problems in Group Theory of Probabilistic Nature |
title_full_unstemmed |
On Some Problems in Group Theory of Probabilistic Nature |
title_sort |
on some problems in group theory of probabilistic nature |
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Penerbit Universiti Putra Malaysia, Serdang |
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2010 |
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http://eprints.utm.my/id/eprint/38011/2/MM%20v.32%282%292010_35_41.pdf http://eprints.utm.my/id/eprint/38011/ http://math.upm.edu.my/dismath/paper/2010/MM%20v.32(2)2010_35_41.pdf |
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