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The mapping torus of an endomorphism Phi of a group G is the HNN-extension G*_G with bonding maps the identity and Phi. We show that a mapping torus of an injective free group endomorphism has the property that its finitely generated subgroups are finitely presented and, moreover, these subgroups are of finite type.
For a fully irreducible automorphism phi of the free group F_k we compute the asymptotics of the intersection number n mapsto i(T,Tphi^n) for trees T,T in Outer space. We also obtain qualitative information about the geometry of the Guirardel core for the trees T and Tphi^n for n large.
We study the loxodromic elements for the action of $Out(F_n)$ on the free splitting complex of the rank $n$ free group $F_n$. We prove that each outer automorphism is either loxodromic, or has bounded orbits without any periodic point, or has a perio
We continue our study of residual properties of mapping tori of free group endomorphisms. In this paper, we prove that each of these groups are virtually residually (finite $p$)-groups for all but finitely many primes$p$. The method involves further
Let $q$ be a prime, $n$ a positive integer and $A$ an elementary abelian group of order $q^r$ with $rgeq2$ acting on a finite $q$-group $G$. The following results are proved. We show that if all elements in $gamma_{r-1}(C_G(a))$ are $n$-Engel in $G
We produce a sequence of markings $S_k$ of Thompsons group $F$ within the space ${mathcal G}_n$ of all marked $n$-generator groups so that the sequence $(F,S_k)$ converges to the free group on $n$ generators, for $n geq 3$. In addition, we give prese