R. M. S. Mahmud

Bio: R. M. S. Mahmud is an academic researcher from University of Bahrain. The author has contributed to research in topics: Word problem (mathematics) & Small cancellation theory. The author has an hindex of 1, co-authored 2 publications receiving 14 citations.

The word problem for small cancellation quotients of groups acting on trees

Abstract: The small cancellation theory over free products with amalgamation and HNN groups is extended to groups acting on trees in which the action with inversions is possible. This will include the case of tree products of groups and treed-HNN groups.

Public Perception of Zoning School Policy in Surakarta Public Senior High Schools

Abstract: By the year in 2017 the implementation of new learner’s acceptance policy (PPDB) in Surakarta Public senior high schools had been changed. In 2017 the policy emphasized with its social accessible one by receiving quota till 20%. however, in 2018 when the policy still being implemented there were changes thus added the zoning system. Ministry of Education and Culture said in 2019 they will enforce the zoning policy and the Poor Certificate of Unable will no longer to be main requirement. Since 2017 Surakarta State Senior High Schools PPDB experienced a lot of polemic and it became public concern. Polemics that occurred from the last two years illustrates there are many people who have different perceptions toward this policy; meaning that although the policy is not necessarily understood by the public yet many differences in interpreting had been occurred. So, this study will analyze on public perception about policy change toward the PPDB 2019 in Surakarta. The research will use qualitative method. Keywords—perception; public policy; policy evaluation

Subgroups of quasi-HNN groups

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.

On invertor elements and finitely generated subgroups of groups acting on trees with inversions

Abstract: 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 g 2 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 ,o rH is in a vertex stabilizer of G.

On the Converse of the Theory of Groups Acting on Trees with Inversions

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.

On preimages of the quasi-treed HNN groups

Abstract: We say that a group G acts on a graph X with inversions if there exist an element g∈G and an edge e∈X such that g transfers e to its inverse $\bar e$, that is, $g\left(e\right) = \bar e$. A group is called a quasi-treed HNN (treed HNN) group if there exists a tree on which the group acts on with inversion (without inversions) and fixing no elements of the tree. The aim of the paper is to prove that if H and G are two groups and p: H→G is an epimorphism such that G is a quasi-treed HNN group (treed HNN), then H is a quasi-treed HNN group (treed HNN). As an application, we show that if N is a normal subgroup of the group G such that the quotient group G/N is a quasi-treed HNN group (or is a treed HNN group), then H is a quasi-treed HNN group (or is a treed HNN group).