How to define the transitive nature of a relation?

I am writing definitions for some terms used in a requirements document. One of the definitions is as follows:

Child account: User account that is created by the account in consideration.

For some requirements I want to define the notion of a descendent account. By that I mean basically the transitive version of a child account.

So far, I'm not getting much further than "child account of a child account", but that does not capture the transitive aspect of the relation.

A descendant of an element is any element that is on a path of child. The important word here, which inherently captures the concept of transitive closure, is 'path'.

This can be defined recursively, meaning the definition of the word involves the use of the word itself in the definition, as:

A descendant is a child or the descendant of a child.

For any two elements, one can establish whether one is a descendant of the other by checking the children (the first part of the definition) or by checking the descendants of those children.

Since this is tagged "mathematics", the definition can use the word recursive. In the terminology of family relations, multiple generations describes transitivity. To be precise, the definition of 'descendant' may clarify if it inclues 'direct child'.
OK, now a short definition:

Descendent account: either a direct or a recursive child account of the account in consideration.

Depending on the targeted audience, a more verbose explanation, even including 'child of child...', may be appropriate.