Lateral axillary buds are not allowed to grow by Auxin.
Auxin is a plant hormone that plays a crucial role in regulating various aspects of plant growth and development, including the growth of lateral axillary buds. Lateral axillary buds are buds that are found in the axil of a leaf, where the leaf meets the stem. These buds have the potential to develop into branches, flowers, or fruits.

Below are the reasons why auxin prevents the growth of lateral axillary buds:

1. Apical dominance: Apical dominance refers to the phenomenon where the terminal bud (the bud at the tip of the stem) inhibits the growth of lateral buds. This is primarily regulated by auxin. The auxin produced in the apical bud inhibits the growth of lateral buds by suppressing their development. This ensures that the plant's energy is focused on the upward growth of the main stem.

2. Inhibition of cytokinin synthesis: Auxin inhibits the synthesis of cytokinins, another plant hormone that promotes the growth of lateral buds. Cytokinins are responsible for stimulating the growth and development of lateral buds into branches. By inhibiting cytokinin synthesis, auxin indirectly prevents the growth of lateral buds.

3. Polar transport of auxin: Auxin can be transported in a polar manner from the shoot apex downwards towards the base of the plant. This polar transport of auxin inhibits the growth of lateral buds along the stem. The concentration of auxin is highest at the shoot apex, which leads to the suppression of lateral bud growth in the lower parts of the stem.

In summary, auxin prevents the growth of lateral axillary buds through apical dominance, inhibition of cytokinin synthesis, and polar transport. These mechanisms ensure that the plant's energy is directed towards the upward growth of the main stem, rather than lateral branching.