# Partially specified elements of a group?

1. Oct 1, 2012

### Stephen Tashi

Is there a technical term in group theory for (what I would call) partially specified elements of a group?

I mean "partially specified" in the following sense:

An elements of a group acts as permuation on the set of elements of the group. So a group element can be considered to be a function that is specified by a set of ordered pairs. Suppose we have a set of ordered pairs of group elements that incompletely specifies a 1-1 function on the group. For example if the group elements are {a,b,c,d} we might have the set of ordered pairs { (a,b),(c,a)} which is missing a specification for (b,?) and (d,?).

If A is a partial specification then reversing the ordered pairs in A give a different partial specification which one might call the inverse specification. If A and B are two partial specification then the product can be defined as the partial specification given by forming the composition of the two mappings, insofar as we can do so from the given ordered pairs in A and B.

2. Oct 1, 2012

### I like Serena

As I know it, it's called a "relation".

From wikipedia: "Formally, a relation is a set of n-tuples of equal degree."

3. Oct 1, 2012

### Stephen Tashi

I agree that it is a relation, but this type of partial specification is more specific than a general relation. A general relation need not even be a subset of the ordered pairs of a function.

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