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- Title
Fixed points of automorphisms preserving the length of words in free solvable groups.
- Authors
Tomaszewski, Witold
- Abstract
Let δ be an automorphism of prime order p of the free group F. Suppose δ has no fixed points and preserves the length of words. By σ := δ we denote the automorphism of the free solvable group $${F_{n}/F_n^{(m)} }$$ induced by δ. We show that every fixed point of σ has the form $${cc^{\sigma} \ldots c^{\sigma^{p-1}}}$$, where $${c\in F_n^{(m-1)}/F_n^{(m)}}$$. This is a generalization of some known results, including the Macedońska-Solitar Theorem [].
- Subjects
FIXED point theory; AUTOMORPHISMS; FREE groups; SOLVABLE groups; NONLINEAR operators
- Publication
Archiv der Mathematik, 2012, Vol 99, Issue 5, p425
- ISSN
0003-889X
- Publication type
Article
- DOI
10.1007/s00013-012-0438-3