On invertor elements and finitely generated subgroups of groups acting on trees with inversions
نویسندگان
چکیده
منابع مشابه
On Invertor Elements and Finitely Generated Subgroups of Groups Acting on Trees with Inversions
An element of a group acting on a graph is called invertor if it transfers an edge of the graph to its inverse. In this paper, we show that if G is a group acting on a tree X with inversions such that G does not fix any element of X, then an element g of G is invertor if and only if g is not in any vertex stabilizer of G and g2 is in an edge stabilizer of G. Moreover, if H is a finitely generat...
متن کاملON QUASI UNIVERSAL COVERS FOR GROUPS ACTING ON TREES WITH INVERSIONS
Abstract. In this paper we show that if G is a group acting on a tree X with inversions and if (T Y ) is a fundamental domain for the action of G on X, then there exist a group &tildeG and a tree &tildeX induced by (T Y ) such that &tildeG acts on &tildeX with inversions, G is isomorphic to &tilde G, and X is isomorphic to &tildeX. The pair (&tilde G &tildeX) is called the quasi universal cover...
متن کاملOn Centralizers of Elements of Groups Acting on Trees with Inversions
A subgroup H of a group G is called malnormal in G if it satisfies the condition that if g ∈G and h∈H, h≠ 1 such that ghg−1 ∈H, then g ∈H. In this paper, we show that if G is a group acting on a tree X with inversions such that each edge stabilizer is malnormal in G, then the centralizer C(g) of each nontrivial element g of G is in a vertex stabilizer if g is in that vertex stabilizer. If g is ...
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and asked if the factor 2 can be dropped. If one translates her approach (which is a slight modification of Howson's) to graph-theoretic terms, it easily shows that the answer is often "yes"in fact, for most U the answer is "yes" for all V. According to Gersten [G], the above problem has come to be known as the "Haana Neumann Conjecture." Using ideas of immersions of graphs originating from Sta...
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We study 2-generated subgroups of groups that act on simplicial trees. We show that any generating pair {g, h} of such a subgroup is Nielsen-equivalent to a pair {f, s} where either powers of f and s or powers of f and sfs−1 have a common fixed point if the subgroup 〈g, h〉 is freely indecomposable. Analogous results are obtained for generating pairs of fundamental groups of graphs of groups. So...
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 2000
ISSN: 0161-1712,1687-0425
DOI: 10.1155/s0161171200002969