PROBABILISTIC STRATEGIES IN GROUP THEOR

Abstract

The aim of this research is to survey,study,understand and contribute to the concept of calculating the probability of a specific feature being in any finite group G, using the regular mathematical definition of probability. This concept is a new trend that connects group theory and probability theory to help solve some problems in group theory. We will study the concept of calculating the probability in any finite group G for the following features: commute of two elements in group G, the non-abelian tensor product for two elements in G when it is equal to the identity element of G, the non-abelian exterior product for two elements in G when it is equal to the identity element of G, and choosing a particular p-block B with respect to the chosen prime number p. Lastly, a new equivalent theorem will be established that calculates the probability of commute of two elements in group G by using the concept of structure constants. Examples of the new theorem will be provided.