# Structure tree

From Groupprops

## Definition

### Definition with symbols

Let be a group acting transitively on a set . A **structure tree** for the action of on is a tree described as follows:

- Put all the elements of at the leaves of the tree
- Find a minimal nontrivial block decomposition for , or equivalently, a decomposition into blocks such that each block contains no proper nontrivial block. Represent each block by a point, and make this set of points form the layer of the tree just above the leaves, such that the children of each block are the elements of that block.
- Now, acts on the set of blocks. Treat this as the new set, again find a minaml block decomposition and make the next layer.
- Keep repeating this process till the action of on the blocks becomes primitive, in which case the next layer will be the root (The block representing the whole of )

## Example

**PLACEHOLDER FOR INFORMATION TO BE FILLED IN**: [SHOW MORE] (I will also put a diagram to make things clearer).