4 papers
On a Combinatorial Characterization of Abelian Group Actions
Carson Gull, Arthur Illidge, Benjamin Mudrak +2
Let be a finite abelian group of order and a finite -set. We give a necessary and sufficient condition on for any to be determined up to isomorphism by certa…
Constructive Proof of Two Characterizations of Arithmetic Equivalence
Shaver Phagan
We prove a formula governing the combinatorics of cyclic group actions and extend a lemma of Hasse to account for ramification. Consequently, we obtain the first constructive proof…
Exceptional Primes in Notions of Arithmetic Similarity
Shaver Phagan
A notion of arithmetic similarity between number fields is defined by requiring equality of some arithmetic statistics over all but finitely many rational primes. The exceptional s…
Corresponding Abelian Extensions of Integrally Equivalent Number Fields
Shaver Phagan
Extensive work has been done to determine necessary and sufficient conditions for a bijective correspondence of abelian extensions of number fields to force an isomorphism of the b…