Symmetric set

In mathematics, a nonempty subset S of a group G is said to be symmetric if In mathematics, a nonempty subset S of a group G is said to be symmetric if where S − 1 = { x − 1 : x ∈ S } {displaystyle S^{-1}={x^{-1}:xin S}} . In other words, S is symmetric if x − 1 ∈ S {displaystyle x^{-1}in S} whenever x ∈ S {displaystyle xin S} . If S is a subset of a vector space, then S is said to be symmetric if it is symmetric with respect to the additive group structure of the vector space; that is, if S = − S = { − x : x ∈ S } {displaystyle S=-S={-x:xin S}} . This article incorporates material from symmetric set on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.