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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2000-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171200002969 |
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| Summary: | 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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| ISSN: | 0161-1712 1687-0425 |