Анотація:
Throughout this paper the actions of groups on
graphs with inversions are allowed. An element g of a group G is
called inverter if there exists a tree X where G acts such that g
transfers an edge of X into its inverse. A group G is called accessible
if G is finitely generated and there exists a tree on which G acts
such that each edge group is finite, no vertex is stabilized by G, and
each vertex group has at most one end.
In this paper we show that if G is a group acting on a tree
X such that if for each vertex v of X, the vertex group Gv of v
acts on a tree Xv, the edge group Ge of each edge e of X is finite
and contains no inverter elements of the vertex group Gt(e) of the
terminal t(e) of e, then we obtain a new tree denoted Xe and is called
a fiber tree such that G acts on Xe. As an application, we show that
if G is a group acting on a tree X such that the edge group Ge for
each edge e of X is finite and contains no inverter elements of Gt(e),
the vertex Gv group of each vertex v of X is accessible, and the
quotient graph G /X for the action of G on X is finite, then G is
an accessible group.