Group (mathematics)
A group is a set equipped with a binary operation that combines any two elements to form a third element. Four conditions called group axioms are satisfied, namely closure, associativity, identity and invertibility. Theory of finite groups was developed in the mid-1980s by Richard Borcherds. It is now the subject of a book, Theory of Finitely Generated Groups, published by Oxford University Press.
About Group (mathematics) in brief
A group is a set equipped with a binary operation that combines any two elements to form a third element. Four conditions called group axioms are satisfied, 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. Groups share a fundamental kinship with the notion of symmetry. For example, a symmetry group encodes symmetry features of a geometrical object. 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. Point groups are used to help understand symmetry phenomena in molecular chemistry. A theory has been developed for finite groups, culminating with the classification of finite simple groups, completed in 2004. The identity element of the group G is often written as 1 or 1G, a notation inherited from the multiplicative identity. The set G is used as a short name for the group, but it is actually a subset of the underlying set G. Along the same lines, shorthand expressions are used when what is actually meant is a group G or an element of G. The group theory of finitely generated groups is an active area in group theory. It studies the different ways in which a group can be expressed concretely, both from a point of view of representation theory and of computational group theory, as well as the theory of simple groups.
The theory of finite groups was developed in the mid-1980s by Richard Borcherds in Mathematicians: An Outer View of the Inner World. It is now the subject of a book, Theory of Finitely Generated Groups, published by Oxford University Press. The book is available in English, French, German, Italian, Spanish, and Portuguese. It can be ordered by clicking here and the English version of this article can be downloaded as a PDF for £1.99 ($3.99) or £2.99 (for a limited time only). It is available on Kindle and other e-book versions of the book, including the Kindle version with a free print-on-demand version of the Kindle edition. The Kindle version also comes with a Kindle app, which lets you download the book for free. The Amazon Kindle version has the option of downloading the book as a download for free, with the option to download the app as a free download for a limited period of time only. The Apple version will be released in the summer of 2014. It will also come with a coupon for a free Kindle book, which will be available in the spring of 2014 for £3.95 ($4.99). The Kindle edition will also include a free copy of the textbook, which is available for download in the Spring of 2015 for £4.49 ($6.99), and a free PDF of the Book of the Month, which comes with the choice of three books, including The Book Of The Month, The Book of The Month and The Book The Book On The Month.
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