Scott Complexity and Adjoining Roots to Finitely Generated Groups
نویسنده
چکیده
We prove a number of generalizations of the fact that any homomorphism of a nonorientable surface group with Euler characteristic −1 to a free group has cyclic image. This is important for our work on Krull dimension of limit groups.
منابع مشابه
Krull Dimension for Limit Groups Iii: Scott Complexity and Adjoining Roots to Finitely Generated Groups
This is the third paper in a sequence on Krull dimension for limit groups, answering a question of Z. Sela. We give generalizations of the well known fact that a nontrivial commutator in a free group is not a proper power to both graphs of free groups over cyclic subgroups and freely decomposable groups. None of the paper is specifically about limit groups.
متن کاملKrull Dimension for Limit Groups Iv: Adjoining Roots
This is the fourth and last paper in a sequence on Krull dimension for limit groups, answering a question of Z. Sela. In it we finish the proof, analyzing limit groups obtained from other limit groups by adjoining roots. We generalize our work on Scott complexity and adjoining roots from the previous paper in the sequence to the category of limit groups.
متن کاملDelzant’s variation on Scott Complexity
We give an exposition of Delzant’s ideas extending the notion of Scott complexity of finitely generated groups to surjective homomorphisms from finitely presented groups.
متن کاملProbability of having $n^{th}$-roots and n-centrality of two classes of groups
In this paper, we consider the finitely 2-generated groups $K(s,l)$ and $G_m$ as follows:$$K(s,l)=langle a,b|ab^s=b^la, ba^s=a^lbrangle,\G_m=langle a,b|a^m=b^m=1, {[a,b]}^a=[a,b], {[a,b]}^b=[a,b]rangle$$ and find the explicit formulas for the probability of having nth-roots for them. Also, we investigate integers n for which, these groups are n-central.
متن کاملTorsion of Abelian Varieties, Weil Classes and Cyclotomic Extensions
Let K ⊂ C be a field finitely generated over Q, K(a) ⊂ C the algebraic closure of K, G(K) = Gal(K(a)/K its Galois group. For each positive integer m we write K(μm) for the subfield of K(a) obtained by adjoining to K all mth roots of unity. For each prime l we write K(l) for the subfield of K(a) obtained by adjoining to K all l−power roots of unity. We write K(c) for the subfield of K(a) obtaine...
متن کامل