the probability that the commutator of two group elements is equal to a given element has been introduced in literature few years ago. several authors have investigated this notion with methods of the representation theory and with combinatorial techniques. here we illustrate that a wider context may be considered and show some structural restrictions on the group.

Double semigroups have two associative operations ◦, • related by the interchange relation: (a • b) ◦ (c • d) ≡ (a ◦ c) • (b ◦ d). Kock [13] (2007) discovered a commutativity property in degree 16 for double semigroups: associativity and the interchange relation combine to produce permutations of elements. We show that such properties can be expressed in terms of cycles in directed graphs with ...

Commutativity of operations is the better way to provide a high degree of concurrency on shared data types. In this short paper, we present a technique to increase concurrency using operational transformations. This technique enforces commutativity even though the operations do not naturally commute. We report our experience on (i) automatically verifying the correctness of this transformation-...

For a given element $g$ of finite group $G$, the probablility that commutator randomly choosen pair elements in $G$ equals is relative commutativity degree $g$. In this paper we are interested studying Dihedral order $2n$ and Quaternion $2^{n}$ for any $n\geq 3$ examine infinite class Moufang Loops Chein type, $M(G,2)$.

We introduce a family of hypergroups, called weakly complete, generalizing the construction complete hypergroups. Starting from given group G, our prescribes β-classes hypergroups and allows some hyperproducts not to be parts, based on suitably defined relation over G. The commutativity degree can related that underlying group. Furthermore, in analogy commutativity, we completeness finite analy...