## Recognizing Simple Groups by Their Codegree Sets

 dc.contributor.advisor Intermont, Michele, 1967- dc.contributor.author Dolorfino, Mallory dc.date.accessioned 2023-04-23T17:19:01Z dc.date.available 2023-04-23T17:19:01Z dc.date.issued 2023-01-01 dc.description 23 p. en_US dc.description.abstract An arithmetic property of a group G is a property that can be expressed solely in terms of numbers. The restrictions that certain arithmetic properties place on the structure of a group is a well-studied and fruitful area of research; two of the most well-known theorems pertaining to arithmetic properties assert that all groups of order 2 are abelian and that all finite groups of odd order are solvable. While both of these theorems arise from a single arithmetic property, namely the order of a group, strong conjectures have been made concerning sets of arithmetic properties. For example, in 2000, Huppert conjectured that if a finite nonabelian simple group H and a finite group G share the same character degree set, then G ∼= H × A for some abelian group A. More recently, a stronger conjecture, often called the codegree version of Huppert’s conjecture, has been posed as question 20.79 in the Kourovka Notebook: if H is a nonabelian simple group and G is a finite group such that H and G have equal codegree sets, then G ∼= H. In other words, nonabelian simple groups are recognizable by their codegree sets. Huppert’s codegree conjecture has been verified for several simple groups, but it has yet to be completely proved. In this paper, we verify this conjecture for the sporadic groups and the simple alternating groups. en_US dc.format.mimetype application/pdf dc.identifier.uri https://cache.kzoo.edu/handle/10920/44298 dc.language.iso en_US en_US dc.publisher Kalamazoo College en_US dc.relation.ispartof Kalamazoo College Mathematics Senior Individualized Projects Collection dc.rights U.S. copyright laws protect this material. Commercial use or distribution of this material is not permitted without prior written permission of the copyright holder. dc.title Recognizing Simple Groups by Their Codegree Sets en_US dc.type Thesis en_US