Alan Roche
Department of Mathematics
University of Oklahoma
Norman, OK 730193103
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 semiexpository 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, 247257.

Four Grouptheoretic Proofs of Wedderburn's Little Theorem
Irish Math. Soc. Bulletin 88 (2021), 5768.

A Tale of Two Cyclicities: Counting in Finite Cyclic Groups and
Finite Fields
(with J. Cohen)
Amer. Math. Monthly 129 (2022), no. 7, 660676.

A Characterization of Cyclic Groups via Indices of Maximal Subgroups
Irish Math. Soc. Bulletin 89 (2022), 6572.

Which Finite Rings Have the Most or Fewest Units?
(with J. Cohen)
Amer. Math. Monthly 129 (2022), no. 8, 717733.

There are Infinitely Many Primes: Two Ringtheoretic Variations on Euclid
Irish Math. Soc. Bulletin 91 (2023), 7376.

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?