Example For example, the standard signature for groups in universal algebra is . (Inversion and unit are needed to get the right notions of homomorphism and so that the group laws can be expressed as equations.) Therefore, a subgroup of a group G is a subset S of G such that: the identity e of G belongs to S (so that S is closed under the identity constant operation); whenever x belongs to S, so does x−1 (so that S is closed under the inverse operation); whenever x and y belong to S, so does (so that S is closed under the group's multiplication operation).
Example For example the standard signature for groups in universal algebra is  (Inversion and unit are needed to get the right notions of homomorphism and so that the group laws can be expressed as equations) Therefore, a subgroup of a group G is a subset S of G such that: the identity e of G belongs to S (so that S is closed under the identity constant operation); whenever x belongs to S, so does x−1 (so that S is closed under the inverse operation); whenever x and y belong to S, so does (so that S is closed under the group's multiplication operation).