In the present paper, we analyze closer the non-Howsonicity of the family of free times free-abelian groups Fn × Z m . On one hand, we give an algorithm to decide, given k 2 finitely generated subgroups H 1 , . . . , H k Fn × Z m , whether the intersection H 1 ∩ • • • ∩ H k is again finitely generated and, in the affirmative case, compute a basis for it. On the second hand, we show that any k-intersection configuration is realizable in Fn × Z m , for n = 2 and m big enough.
The classical result by Dyer-Scott about fixed subgroups of finite order automorphisms of Fn being free factors of Fn is no longer true in Z m × Fn. Within this more general context, we prove a relaxed version in the spirit of Bestvina-Handel Theorem: the rank of fixed subgroups of finite order automorphisms is uniformly bounded in terms of m, n. We also study periodic points of endomorphisms of Z m × Fn, and give an algorithm to compute auto-fixed closures of finitely generated subgroups of Z m × Fn. On the way, we prove the analog of Day's Theorem for real elements in Z m × Fn, contributing a modest step into the project of doing so for any right angled Artin group (as McCool did with respect to Whitehead's Theorem in the free context).
Bangladesh is the land of natural beauty and resources, which has different tourist spot, such as beaches, archaeological sites, religious places, hills and islands, forests and others. Tourism industry is contributing to business and social development, the cultural and environmental quality, and employment and economic growth (Onetiua and Predonua, Procedia Soc Behav Sci 92: 652-655, 2013). Recently, refugee crisis attacked the tourism environment in Cox's Bazar, the most attractive tourist spot in Bangladesh. Recently, refugee crisis attacked the tourism environment in Cox's Bazar, the most attractive tourist spot in Bangladesh. In this context, this study is an attempt by the researchers to sort out the effects of refugee, Rohingya, migration in the tourism capital city of Bangladesh. The specific research objectives of this study are: first, to analyze the present scenario of tourism industry in Bangladesh; second, to examine the effects of refugees in tourism industry of Bangladesh; and third, to find out the challenges and suggest some policy recommendations. In this paper the researchers work on a case study of Cox's Bazar. The researchers follow explanatory research, and uses both qualitative and quantitative method to move on the way of purposes. The researchers use interview method, and follow random sampling from hotel managers, NGO workers and tourists in this study. Tourism is the important means for domestic and foreign remittances. But this industry is facing threats due to refugee issues and failing to maintain a good image. This paper focuses on impacts of refugee crisis, and propose some policy recommendations.
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