We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Fixed subgroups are compressed in surface groups.
- Authors
Zhang, Qiang; Ventura, Enric; Wu, Jianchun
- Abstract
For a compact surface Σ (orientable or not, and with boundary or not), we show that the fixed subgroup, Fix ℬ, of any family ℬ of endomorphisms of π1(Σ) is compressed in π1(Σ), i.e. ( ℬ) ≤ (H) for any subgroup ℬ ≤ H ≤ π1(Σ). On the way, we give a partial positive solution to the inertia conjecture, both for free and for surface groups. We also investigate direct products, G, of finitely many free and surface groups, and give a characterization of when G satisfies that ( ϕ) ≤ (G) for every ϕ ∈ (G).
- Subjects
ENDOMORPHISMS; SUBGROUP growth; INTERSECTION graph theory; MATHEMATICAL analysis; NUMERICAL analysis
- Publication
International Journal of Algebra & Computation, 2015, Vol 25, Issue 5, p865
- ISSN
0218-1967
- Publication type
Article
- DOI
10.1142/S0218196715500228