1k views

### How can we determine associativity of a binary structure from its Cayley table? [duplicate]

Suppose $S$ is a finite set with a binary operation $*$ given by a Cayley table. While the commutativity of $*$ can be determined on the basis of the symmetry of the table across the upper-left to ...
784 views

### How to determine if certain operation is associative based on Cayley table [duplicate]

I have the following table and I don't know how to determine if an operation is associative based on the table. Is there an easy way to do it? Or it's just brute force \begin{array}{|c|c|c|c|c|c|} \...
454 views

### Testing for associativity using the multiplication table (Cayley Table) of an operation. [duplicate]

I seem to recall that there is a relatively easy method for determining the associativity of an operation by using its Cayley table. What is it?
35 views

### Is whether an operation associative obvious by just looking at the operation table? [duplicate]

Let's say you're given an operation table for a certain operation. If you want to know if it's commutative you just look at the diagonal and see if the table is symmetric around it. Now is there ...
870 views

### Just How Strong is Associativity?

A friend of mine is using a lot of algebra that is not associative for an advanced Chemistry project. We were discussing it recently and I found it rather amusing how often she said things like "...
1k views

### Associativity for Magma

Say I have the operation table for a magma. I want to know whether or not the operation is associative. However, associativity is defined for an operation on 3 elements, and the operation table deals ...
6k views

### Verifying if a multiplication table is from a group

I'm asked to verify which of these multiplication tables form a group. I'm having problems to see which of the axioms for a group are violated in each table. In (a), I couldn't find an element $e$ ...
449 views

### How many elements have to verify the associativity property in a group?

If this is a duplicate please mark it down. We know that if $(G,\ast)$ is a group then it must verify the associative property, that is, \forall x,y,z\in G:\quad x\ast(y\ast z)\quad=\quad(x\ast y)\...
### Group of Order $5$
Let $G$ be a group of order $5$ with elements $a, b, c, d, 1$ where $1$ is the identity element. This is the definition of the group. We all know that this can't be a group because any group of order ...