This post continues my effort to write solutions to the problems on this year’s Putnam competition. I previously posted a solution to problem A1. Problem A2 seems like it should have been reasonable for students familiar with abstract algebra, but it could have been tricky for students without much exposure to axiomatic theories.

## On 2012 Putnam Problem A2

**Tagged**abelian groups, associativity, cancellation law, commutativity, groups, problem A2, transitivity