In mathematics, and in particular universal algebra, the concept of n-ary group (also called n-group or multiary group) is a generalization of the concept of group to a set G with an n-ary operation instead of a binary operation. By an n-ary operation is meant any set map f: Gn → G from the n-th Cartesian power of G to G. The axioms for an n-ary group are defined in such a way that they reduce to those of a group in the case n = 2. The earliest work on these structures was done in 1904 by Kasner and in 1928 by Dörnte; the first systematic account of (what were then called) polyadic groups...

Chirality is a property of asymmetry important in several branches of science. The word chirality is derived from the Greek χειρ (kheir), "hand," a familiar chiral object. An object or a system is chiral if it is distinguishable from its mirror image; that is, it cannot be superposed onto it. Conversely, a mirror image of an achiral object, such as a sphere, cannot be distinguished from the object. A chiral object and its mirror image are called enantiomorphs (Greek, "opposite forms") or, when referring to molecules, enantiomers. A non-chiral object is called achiral (sometimes also amphichiral...