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Commutativity degree of Zp ≀ Zpn

Article 7, Volume 01, Issue 01, Winter 2012, Page 41-44 PDF (114 K)

Author

Islamic Azad University,Karaj Branch, Iran.

Abstract

For a nite group G the commutativity degree denote by d(G) and dend:
d(G) =
jf(x; y)jx; y 2 G; xy = yxgj
jGj2
:
In [2] authors found commutativity degree for some groups,in this paper we nd commuta-
tivity degree for a class of groups that have high nilpontencies.

Keywords

Presentation of groups; Finite groups; commutativity degree

References

[1] K. Ahmadidelir, H. Doostie, M. Maghasedi, Fiboncci legth of eciently presented metabelian p-group

, Mathematical Sciences, (5:1) (2011) ,87{100.

[2] H. Doostie, M. Maghasedi, Certain classes of groups with commutativity degree d(G) < 1

2 , Ars

combinatorial, 89 (2008) ,263{270 .

[3] W. H. Gustafson, What is probility that two group elements commute?, Amer. Math. Monthly, 80

(1973), 1031{1034.

[4] M. R. Jones, Muliplcators of p-groups, Math. Z., 127 (1972), 165-166.

[5] M. R. Jones, Some inequalities for the muliplcator of nite group, Math. Soc. 39 (1973), 450{456.

[6] P. Lescot, Isoclinism classes and commutativity degrees of nite groups,J. Algebra , 177 (1995), 847{

869.

[7] M. R. R. Moghaddam ,A. R. Salemkar and K. chiti n-isoclinism classes and n-nilpotency degree of

nite groups ,Algebra colloquium, (12:2) (2005), 255{261.

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