How Can Subgroups Be Defined in Universal Algebra?

[mnb96]

Hi,
how can one define the concept of subgroup in universal algebra? is it possible at all?

The problem is that in universal algebra the concept of group is defined by assigning to the inverse element and to the identity element, respectively an unary-operator and a nullary-operator.

I am not able to use the same trick to describe a subgroup.
Any ideas?

 

[Hurkyl]

You define a subalgebras in exactly the same way you would do it for the familiar examples (e.g. groups): a subalgebra of A is nothing more than a subset S that is closed under all of the algebra operations.