Linked Questions

6
votes
2answers
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 ...
1
vote
3answers
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|} \...
3
votes
1answer
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?
2
votes
1answer
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 ...
14
votes
6answers
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 "...
9
votes
5answers
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 ...
2
votes
3answers
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 $e$ ...
10
votes
3answers
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)\...
7
votes
4answers
561 views

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 ...
1
vote
1answer
50 views

Extracting set properties from the Cayley Table to easily prove associativity

I am aware of Light's associativity test for Cayley tables, but I am wondering, is there a clever way to deduce associativity from the set's properties / presentation that permits one to not have ...