We can view braids mathematically as n strings hanging from a horizontal bar. Each piece of string runs downward and can cross neighboring strings. In the 1920s Emil Artin observed that braids of n strings form an algebraic group. To “multiply” two braids, we append the bottom of one braid with the top of another braid. The identity element in this group…

# Tag: group

## Is this the Cayley table of a group? (Part 2)

In my previous post I posed the following question: suppose you are given a table for a binary operation such that there is a two-sided identity, every element has a two-sided inverse, and the table is a Latin square (that is, each symbol occurs exactly once in each row and each column). Is it the Cayley table of a…

## Is this the Cayley table of a group? (Part 1)

A math major in our department business major asked an interesting question the other day. The student’s abstract algebra class was working with Cayley tables. The class was given a table for a binary operation and was asked to check if it was a group. Given a table it is easy to check that the…