This paper describes a relation between the practice of Malay food cover weaving and mathematics. The cover, known as tudung saji, is woven using a specific technique called triaxial or hexagonal weave. Its tessellated parallelograms form an illusion of three dimensional cubes that are found interesting in mathematical studies of symmetrical patterns using group theory. Some of the properties of triaxial template patterns of order n3 are also discussed in this paper.
An extension of the concept of commutativity degree named the probability that an element of a group fixes a set was introduced in 2013. Suppose is a metacyclic 5-group and is the set of all ordered pairs (x,y) in G*G such that lcm(|x|,|y|)=5, xy=yx and x is not equal to y. In this paper, the probability that an element of a metacyclic 5-group fixes the set is computed by using conjugation action.
Let be a metacyclic 3-group and let be a non-empty subset of such that . The generalized commuting and non-commuting graphs of a group is denoted by and respectively. The vertex set of the generalized commuting and non-commuting graphs are the non-central elements in the set such that where Two vertices in are joined by an edge if they commute, meanwhile, the vertices in are joined by an edge if they do not commute.
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