Parole chiave

• word problem
• automata group

Abstract The membership subgroup problem asks whether an element in a group belongs to a fixed subgroup. This gives rise to a formal language and, in the case of stabilizers, to a graph-theoretic interpretation. After defining groups described by automata, we will study the membership languages for stabilizers in this class. In particular, we will make use of Lindenmayer’s systems, which were originally introduced in biology, but recently have successfully been exploited in combinatorial group theory.