4 papers
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…
Echeloned saturation and forcing axioms
Shimon Garti
Addressing a question of Paul Larson we prove the following statement. If Chang's conjecture fails, Martin's axiom holds and the continuum is greater than , there are no…
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…
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.