Factorizations of finite groups by conjugate subgroups which are solvable or nilpotent

We consider factorizations of a finite group $G$ into conjugate subgroups, $G=A^{x_{1}}\cdots A^{x_{k}}$ for $A\leq G$ and $x_{1},\ldots ,x_{k}\in G$, where $A$ is nilpotent or solvable. First we exploit the split $BN$-pair structure of finite simple groups of Lie type to give a unified self-contained proof that every such group is a product of four or three unipotent Sylow subgroups. Then we derive an upper bound on the minimal length of a solvable conjugate factorization of a general finite group. Finally, using conjugate factorizations of a general finite solvable group by any of its Carter subgroups, we obtain an upper bound on the minimal length of a nilpotent conjugate factorization of a general finite group

Minimal length factorizations of finite simple groups of Lie type by unipotent Sylow subgroups

We prove that every finite simple group G of Lie type satisfies G = UU−UU − where U is a unipotent Sylow subgroup of G and U − is its opposite. We also characterize the cases for which G = UU−U. These results are best possible in terms of the number of conjugates of U in the above factorizations

NATURE-BASED SUBURBAN LEISURE OPPORTUNITIES WITHIN THE ORADEA METROPOLITAN AREA

Over the past 15 years, the periurban area in the proximity of Oradea has been accredited as a place of great attraction for the urbanites eager to move to the countryside, taking advantage of the natural resources, numerically generous and possessing an ecological quality. On such a background, these urbanites or tourists have come into contact and continue to discover these natural resources from the point of view of their new qualities, namely people motivated to do thematic tourism. This study seeks to know in detail the potential of the 11 communes and their related villages in the Oradea Metropolitan Area (OMA) and what they provide for weekend-type activities or forms of tourism based on discovery and leisure. The researched area has various natural resources, but diversity is configured according to the environment and morpho-hydrography specific for the hilly, plain and hilly-plain contact area relief. The inventory of local resources (8 categories) prone to nature-based tourism is dominated by protected areas, rivers and lakes for fishing, deciduous forests and associated hay fields as well as the hilly relief in the eastern part of the area. The expression of the attractiveness of local nature for leisure tourism is given by the attractiveness index, which at the OMA level is 87.47 points, with an encouraging maximum of 11.67 points (out of a maximum of 25 points). The detail of the distribution and the natural resources attraction weight can be found in the four thematic maps

Oradea Metropolitan Area as a Space of Interspecific Relations Triggered by Physical and Potential Tourist Activities

Metropolitan areas provide many opportunities to spend quality outdoor leisure time as well as to discover many cultural attractions. Sprawl occurs in Romania quite rapidly, encouraged by the construction of ring roads around many cities and their expansion into metropolitan areas. The current paper aims to identify metropolitan tourism models based on which tourist flows can be sustainably reoriented within rural Oradea Metropolitan Area (OMA) given their the tourist potential level (i.e., very low, low, average, high). The tourist potential was scaled based on the Methodology for the Analysis of a Territory’s Tourist Potential, which stands as a law published in the Official Monitor of the 14th of June 2016. The study indicates that most tourist activity develops in the OMA southern part in Sânmartin commune, thus unsustainably capturing all tourist flows of the rural OMA. Natural and man-made tourist attractions’ territorial concentrations were emphasized in the communes from the south and northern OMA, but there are major territorial dysfunctions in terms of technical endowment and tourist infrastructure supply. The three emerged models refer to the medical–recreational and eco–residential wellness network, discovery eco-holiday, and co-visit and marginal community

Oradea Metropolitan Area as a Space of Interspecific Relations Triggered by Physical and Potential Tourist Activities

Metropolitan areas provide many opportunities to spend quality outdoor leisure time as well as to discover many cultural attractions. Sprawl occurs in Romania quite rapidly, encouraged by the construction of ring roads around many cities and their expansion into metropolitan areas. The current paper aims to identify metropolitan tourism models based on which tourist flows can be sustainably reoriented within rural Oradea Metropolitan Area (OMA) given their the tourist potential level (i.e., very low, low, average, high). The tourist potential was scaled based on the Methodology for the Analysis of a Territory’s Tourist Potential, which stands as a law published in the Official Monitor of the 14th of June 2016. The study indicates that most tourist activity develops in the OMA southern part in Sânmartin commune, thus unsustainably capturing all tourist flows of the rural OMA. Natural and man-made tourist attractions’ territorial concentrations were emphasized in the communes from the south and northern OMA, but there are major territorial dysfunctions in terms of technical endowment and tourist infrastructure supply. The three emerged models refer to the medical–recreational and eco–residential wellness network, discovery eco-holiday, and co-visit and marginal community