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  • অত্যন্ত দু:খের সাথে নির্জনমেলা পরিবারের পক্ষ থেকে জানানো যাচ্ছে যে, কিছু অসাধু ব্যক্তি নির্জনমেলার অগ্রযাত্রায় প্রতিহিংসা পরায়ন হয়ে পূর্বের সকল ডাটাবেজ ধ্বংস করে দিয়েছে যা ফোরাম জগতে অত্যন্ত বিরল ঘটনা। সকল প্রকার প্রতিরক্ষা ব্যবস্থা রাখা সত্বেও তারা এরকম ধ্বংসাত্মক কর্মকান্ড সংঘটিত করেছে। তাই আমরা আবার নুতনভাবে সবকিছু শুরু করছি। আশা করছি, যে সকল সদস্যবৃন্দ পূর্বেও আমাদের সাথে ছিলেন, তারা ভবিষ্যতেও আমাদের সাথে থাকবেন, আর নির্জনমেলার অগ্রনী ভূমিকায় অবদান রাখবেন। সবাইকে সাথে থাকার জন্য আন্তরিক কৃতজ্ঞতা প্রকাশ করছি। বি:দ্র: সকল পুরাতন ও নুতন সদস্যদের আবারো ফোরামে নুতন করে রেজিস্ট্রেশন করতে হবে। সেক্ষেত্রে পুরাতন সদস্যরা তাদের পুরাতন আইডি ও পাসওয়ার্ড দিয়ে রেজিস্ট্রেশন করতে পারবেন।

group

In mathematics, a group is an algebraic structure consisting of a set of elements equipped with a binary operation which combines any two elements to form a third element. To be a group, this operation must satisfy four conditions called the group axioms, namely closure, associativity, identity and invertibility. One of the most familiar examples of a group is the set of integers together with the addition operation, but the abstract formalization of the group axioms, detached as it is from the concrete nature of any particular group and its operation, applies much more widely. It allows entities with highly diverse mathematical origins in abstract algebra and beyond to be handled in a flexible way while retaining their essential structural aspects. The ubiquity of groups in numerous areas within and outside mathematics makes them a central organizing principle of contemporary mathematics.Groups share a fundamental kinship with the notion of symmetry. For example, a symmetry group encodes symmetry features of a geometrical object: the group consists of the set of transformations that leave the object unchanged and the operation of combining two such transformations by performing one after the other. Lie groups are the symmetry groups used in the Standard Model of particle physics; Poincaré groups, which are also Lie groups, can express the physical symmetry underlying special relativity; and point groups are used to help understand symmetry phenomena in molecular chemistry.
The concept of a group arose from the study of polynomial equations, starting with Évariste Galois in the 1830s. After contributions from other fields such as number theory and geometry, the group notion was generalized and firmly established around 1870. Modern group theory—an active mathematical discipline—studies groups in their own right. To explore groups, mathematicians have devised various notions to break groups into smaller, better-understandable pieces, such as subgroups, quotient groups and simple groups. In addition to their abstract properties, group theorists also study the different ways in which a group can be expressed concretely, both from a point of view of representation theory (that is, through the representations of the group) and of computational group theory. A theory has been developed for finite groups, which culminated with the classification of finite simple groups, completed in 2004. Since the mid-1980s, geometric group theory, which studies finitely generated groups as geometric objects, has become a particularly active area in group theory.

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