Robert Heffernan

Dept. of Mathematics, MTU, Cork, Ireland

Research

My research interests are primarily in the area of group theory.

I have an interest in the theory of finite p-groups and the theory of automorphisms of finite groups. I am especially interested in the commuting probability of finite groups and related concepts. As well as this, I have some interest in the ordinary representation theory (or at least, the character theory) of finite groups.

More recently, I have developed an interest in geometric group theory and, in particular, the theories of automatic groups and graph-automatic groups.

Publications

  • R. Heffernan, D. MacHale: Missing subgroups (in preparation).
  • R. Heffernan, D. MacHale: Comparing large values of commutativity ratios in finite groups (in preparation).
  • R. Heffernan, B. McCann: Minimal embeddings of finite cyclic groups (in preparation).
  • R. Heffernan, N. Lord, D. MacHale: Euler's prime-producing polynomial revisited in The Mathematical Gazette, Volume 108, Issue 571, 69–77 (2024).
  • R. Heffernan, D. MacHale: The genesis of a conjecture in number theory in Bulletin of the Irish Mathematical Society, 93, 39–41 (2024).
  • R. Heffernan, D. MacHale: Finite groups with at most nine non-central conjugacy classes in Mathematical Proceedings of the Royal Irish Academy 124 (1), 33–46 (2024).
  • R. Heffernan, D. MacHale: Some shorter proofs for p-groups (Classroom note) in Bulletin of the Irish Mathematical Society, 86, 107–108 (2020).
  • R. Heffernan, B. McCann: Minimal embeddings of small finite groups in International Journal of Group Theory, 9 (3), 157–183 (2020).
  • R. Heffernan, D. MacHale: Values of f(G) for groups G of odd order with \(\Pr(G) \geq \frac{11}{75}\) in Bulletin of the Irish Mathematical Society, 85, 17–20 (2020).
  • R. Heffernan, D. MacHale: On the order of a smallest group with a given representation degree in Bulletin of the Irish Mathematical Society, 84, 21–24 (2020).
  • R. Heffernan, D. MacHale, B. McCann: Cayley's theorem revisited: Embeddings of small finite groups in Mathematics Magazine, 91 (2), 103–111 (2018).
  • R. Heffernan, D. MacHale, Á. Ní Shé: Central factor groups and commutativity in Mathematical Proceedings of the Royal Irish Academy, Vol. 117A (2), 63–75 (2017).
  • R. Heffernan, D. MacHale, Á. Ní Shé: Restrictions on commutativity ratios in finite groups in the International Journal of Group Theory, 3 (4), 1–12 (2014).
  • J. Curran, R. Heffernan and D. MacHale: On the Order of the Automorphism Group of a Finite Group in Communications in Algebra, 39 (10), 3616–3624, (2011).
  • C. Freuder, R. Heffernan, R. J. Wallace and N. Wilson: Lexicographically-ordered Constraint Satisfaction Problems in Constraints, 15 (1), 1–28 (2010).
  • R. Heffernan and D. MacHale: On the sum of the character degrees of a finite group in Mathematical Proceedings of the Royal Irish Academy, 108A (1), 57–63 (2008).
  • C. Freuder, R. Heffernan and R. J. Wallace: Ordinal constraint satisfaction in The Proceedings of 5th International Workshop on Soft Constraints, 2003.