Commutativity degree of $\mathbb{Z}_p$≀$\mathbb{Z}_{p^n}

الموضوعات :

M. Maghasedi ¹ (Islamic Azad University, Karaj Branch, Iran)

تاريخ الإرسال : 07 الأحد , صفر, 1433 تاريخ التأكيد : 07 الأحد , صفر, 1433 تاريخ الإصدار : 08 الخميس , ربيع الثاني, 1433

الکلمات المفتاحية: Presentation of groups, Finite groups, commutativity degree,

ملخص المقالة :

For a nite group G the commutativity degree denote by d(G) and dend:$$d(G) =\frac{|\{(x; y)|x, y\in G,xy = yx\}|}{|G|^2}.$$ In [2] authors found commutativity degree for some groups,in this paper we nd commutativity degree for a class of groups that have high nilpontencies.

المصادر:

[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 finite groups ,Algebra colloquium, (12:2) (2005), 255-261.