0
votes
1answer
34 views

homomorphism problem

The monoids $(S,\min)$ and $(T,\min)$, where $S = \{3,4,5,6\}$ and $T = \{1,2,3,4,5,6\}$ and $\min$ is the minimum function of two integers. Let the function $f:S \to T$ be defined by $f(x) = x-1$; ...
4
votes
2answers
200 views

An analogy between subgroups and equivalence relations.

I have noticed a certain analogy between subgroups of a group $G$ and equivalence relations on a set $X$. I would like to know if there's an explanation for this analogy or a common generalization of ...
0
votes
1answer
87 views

Can a group be defined in terms of a relation on a set?

Wikipedia defines a group as "an algebraic structure consisting of a set together with an operation that combines any two of its elements to form a third element." I keep thinking that there is a ...