Embedding Properties in Central Products

Abstract

In group theory, we study ways to get new groups from old groups, and we study properties of subgroups and further characterizations of subgroups in various groups. Edouard Goursat determined a method to characterize the subgroups of a direct product of two groups, and many group theorists use his characterization to help understand subgroups of direct products. Central products are direct products with amalgamated centers. The amalgamated centers are the intersection of the centers of the groups whose product is being taken, and it contains the intersection of the groups themselves. For this project, we worked to accomplish the characterization of pronormal subgroups in central products, which is an extension of previous work from where Lewis, Almousa, and Elert characterized normal, subnormal, and abnormal subgroups in central products.