Advances and Applications in Discrete Mathematics
Volume 10, Issue 2, Pages 95 - 102
(October 2012)
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A NOTE ON ACCESSIBLE GROUPS
Rasheed. M. S. Mahmood
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Abstract: A finitely generated group is called an accessible group if there exists a tree on which the group acts without inversions such that each edge group is finite, no vertex is stabilized by the group, and each vertex group has at most one end. In this paper, we show that if H is a subgroup of the accessible G, then
(1) If H is of finite index in G, then H is accessible.
(2) If H is finite and normal, then the quotient group G/H is accessible. |
Keywords and phrases: ends of groups, groups acting on trees, accessible groups. |
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