Some applications of metacyclic 2-groups of negative type

The probability that two random elements commute in a finite group G is the quotient of the number of commuting elements and |G|2. Consider a set S consisting of all subsets of commuting elements of G of size two that are in the form (a,b) where a and b commute and lcm(|a|,|b|)=2. The probability th...

全面介紹

Saved in:
書目詳細資料
Main Authors: Saleh Omer, Sanaa Mohamed, Sarmin, Nor Haniza, Erfanian, Ahmad
格式: Article
出版: Thailands Natl Science & Technology Development Agency 2016
主題:
在線閱讀:http://eprints.utm.my/id/eprint/66753/
http://dx.doi.org/10.2306/scienceasia1513-1874.2016.42S.001
標簽: 添加標簽
沒有標簽, 成為第一個標記此記錄!
實物特徵
總結:The probability that two random elements commute in a finite group G is the quotient of the number of commuting elements and |G|2. Consider a set S consisting of all subsets of commuting elements of G of size two that are in the form (a,b) where a and b commute and lcm(|a|,|b|)=2. The probability that a group element fixes S is the number of orbits under the group action on S divided by |S|. In this paper, the probability that a group element fixes a set S under regular action is found for metacyclic 2-groups of negative type of nilpotency class two and of class at least three. The results obtained from the sizes of the orbits are then applied to the generalized conjugacy class graph.