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

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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.

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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.

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Aoibhe Redux

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

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The Marvelous Ms. Mabel

Two views (the second in slow motion) of a jump by Aoibhe's pal, Mabel. She gets a small deduction for not quite sticking the landing. And some of the humans in the household are nervous about her use of the mirror which is somewhat dilapidated (like one of the humans). But wow—what a maneuver!