group

1. (group theory) A set with an associative binary operation, under which there exists an identity element, and such that each element has an inverse.Examples: "Throughout this section, we shall assume the existence of finitely presented groups with unsolvable word problem."; "In this chapter we give some examples of Fuchsian groups. The most interesting and important ones are the so-called "arithmetic" Fuchsian groups, i.e., discrete subgroups of PSL(2,R) obtained by some "arithmetic" operations. One such construction we have already seen: if we choose all matrices of SL(2,R) with integer coefficients, then the corresponding elements of PSL(2,R) form the modular group PSL(2,Z)."; "2007, Zhong-Qi Ma, Group Theory for Physicists, World Scientific, page 277, In Chap. 4 the fundamental concepts on Lie groups have been introduced through the SO(3) group and its covering group SU(2)."

2. (geometry, archaic) An effective divisor on a curve.

3. (astronomy) A small number (up to about fifty) of galaxies that are near each other.

4. (chemistry) A column in the periodic table of chemical elements.

5. (chemistry) A functional group.Examples: "Nitro is an electron-withdrawing group."

6. (sociology) A subset of a culture or of a society.