3 papers
math.RA2026
Elementary proofs of ring commutativity theorems
Michael Kinyon, Desmond MacHale
Jacobson's commutativity theorem says that a ring is commutative if, for each , for some . Herstein's generalization says that the condition can be weakened to…
math.GR2017
Minimal embeddings of small finite groups
Robert Heffernan, Des MacHale, Brendan McCann
We determine the groups of minimal order in which all groups of order n can embedded for 1 < n < 16. We further determine the order of a minimal group in which all groups or order…
math.GR2009
Minimal odd order automorphism groups
Peter Hegarty, Desmond MacHale
We show that 3^7 is the smallest order of a non-trivial odd order group which occurs as the full automorphism group of a finite group.