On The Exterior Degree of Some Finite p-Groups

  • Fadila Normahia Abd Manaf
  • Nor Haniza Sarmin
  • Nor Muhainiah Mohd Ali
  • Ahmad Erfanian
Keywords: commutativity degree, exterior square, finite group

Abstract

In any finite group G, the commutativity degree of G (denoted by P(G)) is the probability that two randomly chosen elements of G commute. P(G) has been introduced by Erdos and Turan (1968) for symmetric groups. Gustafson (1973) did the same for compact groups while MacHale (1974) determined the commutativity degree of finite rings. The exterior square of G, denoted as G ˄ G, is defined as G ˄ G = G7G/d(G) where (G7G) is the nonabelian tensor square of G and d(G) is a subgroup of G generated by x7x for all xdG. Recently, Niroomand and Rezaei (2011) give some relations between the concept of exterior square and commutativity degree by defining the exterior degree of a finite group G, denoted as P/(G), to be the probability for two elements g and g' in G such that g / g' = 1 where 1/, is the identity of G/G. In this paper, the exterior degree of some finite groups is presented.

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Author Biographies

Fadila Normahia Abd Manaf

Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia

Nor Haniza Sarmin

Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia

Nor Muhainiah Mohd Ali

Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia

Ahmad Erfanian

Department of Pure Mathematics, Faculty of Mathematical Science and Center of Excellence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad, Mashhad, Iran

Published
2019-01-19
How to Cite
Abd Manaf, F. N., Sarmin, N. H., Mohd Ali, N. M., & Erfanian, A. (2019). On The Exterior Degree of Some Finite p-Groups. Journal of Science and Mathematics Letters, 4(2), 69-74. Retrieved from https://ejournal.upsi.edu.my/index.php/JSML/article/view/394