Fixed points of automorphisms preserving the length of words in free solvable groups

Abstract

Abstract. Let δ be an automorphism of prime order p of the free group Fn. Suppose δ has no fixed points and preserves the length of words.

Self-Similar Automorphisms of a Free Group of Countable Rank

“…This work is inspired by research on automorphisms permuting generators in free groups of finite rank (cf. [9], [15]). The following example shows the relationship between self-similar automorphisms and automorphisms permuting generators in the free group of rank two.…”