Alan Roche Department of Mathematics University of Oklahoma Norman, OK 73019-3103 Office: PHSC 1102 Email: aroche (at) ou (dot) edu

---

Welcome! The picture is not me: it's Aoibhe, pronounced A V as in the letters.

Aoibhe studies CATegory theory. My research area is representation theory, mainly representations of p‒adic groups, a subject with close ties to number theory. In recent years, however, I've found myself writing semi-expository pieces on more elementary topics. Some are listed below.

---

Recent Notes and Papers

• A Note on Dual Modules and the Transpose (with T. Madsen and C. R. Vinroot)
  Arch. Math. (Basel) 114 (2020), no. 3, 247-257.


• Four Group-theoretic Proofs of Wedderburn's Little Theorem
  Irish Math. Soc. Bulletin 88 (2021), 57-68.


• A Tale of Two Cyclicities: Counting in Finite Cyclic Groups and Finite Fields (with J. Cohen)
  Amer. Math. Monthly 129 (2022), no. 7, 660-676.


• A Characterization of Cyclic Groups via Indices of Maximal Subgroups
  Irish Math. Soc. Bulletin 89 (2022), 65-72.


• Which Finite Rings Have the Most or Fewest Units? (with J. Cohen)
  Amer. Math. Monthly 129 (2022), no. 8, 717-733.


• There are Infinitely Many Primes: Two Ring-theoretic Variations on Euclid
  Irish Math. Soc. Bulletin 91 (2023), 73-76.


• Another Short Proof that Rational Algebraic Integers are Integers
  To appear in Math. Mag. 97 (2024), no. 3.

---

Aoibhe Redux

O furless biped, why dost thou point at me the dark rectangle which maketh that clicking sound?

---