On Isomorphism Theorems and Characterizing Properties of Groups

In group theory, understanding properties of groups is essential. However, in some circumstances determining the properties of groups is challenging because of the structure or ambiguity of a group. The Isomorphism Theorems provide a solution to this challenge. When two groups are isomorphic to one another, it is said that those two groups have the same properties as each other. Given a group G and subgroups N and K of G, the First, Second, and Third Isomorphism Theorems allow us to find isomorphisms between different groups. In this study, we examine the proofs for the Isomorphism Theorems to understand which groups we can claim are isomorphic to each other.https://ecommons.udayton.edu/stander_posters/2811/thumbnail.jp