defining group
71Outline of algebraic structures — In universal algebra, a branch of pure mathematics, an algebraic structure is a variety or quasivariety. Abstract algebra is primarily the study of algebraic structures and their properties. Some axiomatic formal systems that are neither… …
72Van Kampen diagram — In the mathematical area of geometric group theory, a van Kampen diagram is a planar diagram used to represent the fact that a particular word among the generators of a group given by a group presentation represents the identity element in that… …
73mathematics — /math euh mat iks/, n. 1. (used with a sing. v.) the systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically. 2. (used with a sing. or pl. v.) mathematical procedures,… …
74Differentiable manifold — A nondifferentiable atlas of charts for the globe. The results of calculus may not be compatible between charts if the atlas is not differentiable. In the middle chart the Tropic of Cancer is a smooth curve, whereas in the first it has a sharp… …
75Christianity — /kris chee an i tee/, n., pl. Christianities. 1. the Christian religion, including the Catholic, Protestant, and Eastern Orthodox churches. 2. Christian beliefs or practices; Christian quality or character: Christianity mixed with pagan elements; …
76Direct sum of modules — For the broader use of the term in mathematics, see Direct sum. In abstract algebra, the direct sum is a construction which combines several modules into a new, larger module. The result of the direct summation of modules is the smallest general… …
77Music of Israel — …
78Algebraic structure — In algebra, a branch of pure mathematics, an algebraic structure consists of one or more sets closed under one or more operations, satisfying some axioms. Abstract algebra is primarily the study of algebraic structures and their properties. The… …
79Genocides in history — Genocide is the mass killing of a group of people, as defined by Article 2 of the Convention on the Prevention and Punishment of the Crime of Genocide (CPPCG) as any of the following acts committed with intent to destroy, in whole or in part, a… …
80arts, East Asian — Introduction music and visual and performing arts of China, Korea, and Japan. The literatures of these countries are covered in the articles Chinese literature, Korean literature, and Japanese literature. Some studies of East Asia… …
