Advances and Applications in Discrete Mathematics
Volume 13, Issue 2, Pages 109 - 116
(April 2014)
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ON THE QUOTIENTS OF THE FUNDAMENTAL GROUPS OF QUASI-GRAPHS OF GROUPS
R. M. S. Mahmood
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Abstract: A graph is called a quasi-graph if the case of an edge of the graph equals its inverse is allowed. A graph of groups is called a quasi-graph of groups if the corresponding graph is a quasi-graph. 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. In this paper, we show that if G is a fundamental group of a quasi-graph of groups and if H is a finite normal subgroup of G containing no inverter elements, then the quotient group is a fundamental group of a quasi-graph of groups. |
Keywords and phrases: quasi-graphs of groups, groups acting on trees. |
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