On Invertor Elements and Finitely Generated Subgroups of Groups Acting on Trees with Inversions
نویسندگان
چکیده
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 generated subgroup of G, then H contains an invertor element or some conjugate of H contains a cyclically reduced element of length at least one on which H is not in any vertex stabilizer of G, or H is in a vertex stabilizer of G.
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ON QUASI UNIVERSAL COVERS FOR GROUPS ACTING ON TREES WITH INVERSIONS
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