6,575 research outputs found

    A Note On Transversals

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    Let GG be a finite group and HH a core-free subgroup of GG. We will show that if there exists a solvable, generating transversal of HH in GG, then GG is a solvable group. Further, if SS is a generating transversal of HH in GG and SS has order 2 invariant sub right loop TT such that the quotient S/TS/T is a group. Then HH is an elementary abelian 2-group.Comment: 7 page

    Sustainability of Agricultural Development in Jhabua District of Madhya Pradesh

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    The impact of modernisation through industrialisation has resulted in environmental and ecological degradation in peripheral resource hinterlands in hilly regions. The tribes, unable to find economic sustenance in forest habitats, have, in majority, adapted to extensive agricultural practices as main economic base of the community. The anthropogenic forces have dominance and succession over the resources through modern forestry, mining and quarrying activities and the industrial, trade and service activities. The increasing pressure of population of the local communities on agriculture and the drought condition and fluctuating rainfall has led to social and economic unsustainability of the agriculture and resulted in increasing food and livelihood insecurities, poverty and increasing inaccessibility to the local resources and modern economic activities. It is necessary to restore the agricultural ecosystems in the hilly regions through conservation and development of resources and increase the resource use efficiencies and farm productivities of different cropping systems through horizontal and vertical diversification, integration and specialization of the organic productive systems, so as to increase the cropping and ecological intensities to minimize the environmental risks and economic uncertainties at the farm levels in different activity zones in geographical landscape. The research work under Ph. D programme has attempted to develop a sustainable development model of agriculture for hilly and tribal areas. The agricultural development in Jhabua district has been studied in view of population ecology, farm ecology and farm productivity in different ecologic-economic zones. The study has used inter-regional analysis of the agricultural ecosystems in inter-tahsil analysis in macro ecological-economic framework and with the sample villages in different activity zones in the sample tahsils in micro ecologic-economic framework. The eco-regional modeling of agricultural system has been made by selecting indicators of its subsystems, e.g. population ecology, environment, infrastructure and agricultural ecology with the structural variables for agro-ecosystem analysis and evaluation of the status in the study periods 1990-91 and 2004-05. The composite indices have been used for analysis of regional variation in the level of agricultural development and identify the instrumental variables for strategic policy decisions for agro-eco restoration and faster economic growth in functional and spatial framework. The technique of factor analysis has been used for this purpose. At the micro-levels, the village ecosystems and farm ecosystems have been studied to investigate the problems and prospects of the development by selecting representative sample villages in geographical landscape framework in different activity zones with increasing distance from the main market centres to the hinterland agricultural, animal husbandry and forestry zones in hierarchic order. Public opinion and perceptions have been analysed for identification of the priorities for micro-ecologic and economic development in the region. The research work provides a strategic framework for sustainable development of agriculture in Jhabua district in particular in grass-root approach to regional development and provides a model framework for the tribal areas in India in general.Agricultural sustainability, agricultural ecosystem, eco-regional modelling

    Solvable and Nilpotent Right Loops

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    In this paper the notion of nilpotent right transversal and solvable right transversal has been defined. Further, it is proved that if a core-free subgroup has a generating solvable transversal or a generating nilpotent transversal, then the whole group is solvable.Comment: arXiv admin note: substantial text overlap with arXiv:1307.539
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