Journal Article•
On quasi HNN groups
About: This article is published in Kuwait Journal of Science & Engineering.The article was published on 2002-01-01 and is currently open access. It has received 6 citations till now.
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TL;DR: In this article, the subgroup theorem for groups acting on======trees with inversions was extended to quasi-HNN groups, and the main technique used is the sub-group theorem.
Abstract: We extend the structure theorem for the subgroups of the class of
HNN groups to a new class of groups called quasi-HNN groups. The
main technique used is the subgroup theorem for groups acting on
trees with inversions.
4 citations
TL;DR: In this article, it was shown that if a group acting on a graph X with inversions has a presentation induced by a fundamental domain for the action of G on X, then X is a tree.
Abstract: In this paper we show that if G is a group acting on a graph X with inversions such that G has a presentation induced by a fundamental domain for the action of G on X, then X is a tree.
2 citations
Journal Article•
TL;DR: In this paper, the authors introduced the concepts of a quasi graph of groups and its fundamental group, and showed that the fundamental group of such a graph is a quasi HNN group.
Abstract: A graph is called a quasi graph if the possibility of an edge of the graph being equal to its inverse is not excluded. Quasi HNN groups are a new generalizations of HNN groups. In this paper we introduce the concepts of a quasi graph of groups and its fundamental group, and show that the fundamental group of a quasi graph of groups is a quasi HNN group. The embedding theorem for the fundamental group of a quasi graph of groups is formulated and proved. Furthermore, we find the structures of groups induced by the vertices of a quasi graph of groups.
1 citations
TL;DR: It is shown that if G ∗ is a quasi-HNN group of base G , then either any two conjugates of G are identical or their intersection is contained in a conjugate of an associated subgroup of G .
Abstract: Quasi-HNN groups can be characterized as a generalization of HNN
groups. In this paper, we show that if G ∗ is a quasi-HNN
group of base G , then either any two conjugates of G are
identical or their intersection is contained in a conjugate of
an associated subgroup of G .
1 citations
TL;DR: In this paper, the authors show that if G is a group acting on a tree X with inversions such that each edge stabilizer is malnormal in G, then the centralizer C ( g ) of each nontrivial element g of G is in a======vertex stabilizer if g is in that vertex stabilizer.
Abstract: A subgroup H of a group G is called malnormal in G if it satisfies the condition that if g ∈ G and h ∈ H , h ≠ 1
such that g h g − 1 ∈ H , then g ∈ H . In this paper, we show
that if G is a group acting on a tree X with inversions such
that each edge stabilizer is malnormal in G , then the
centralizer C ( g ) of each nontrivial element g of G is in a
vertex stabilizer if g is in that vertex stabilizer. If g is
not in any vertex stabilizer, then C ( g ) is an infinite cyclic
if g does not transfer an edge of X to its inverse. Otherwise,
C ( g ) is a finite cyclic of order 2.