**MSC:**- 68Q45 Formal languages, See also {03D05, 20M35, 94A45}
- 68Q70 Algebraic theory of automata, See also {18B20, 20M35}

extendable string within a language. It demonstrates that every

language that has such an iteratively extendable string $z$

contains infinitely many strings whose length is divisible by the

length of $z$. Some consequences and applications of this result

are given.

This work was supported by GACR grant GA201/04/0441

and GACR grant GA102/05/H050.