Locally compact examples of these algebraic structures can be assigned Haar measures. All possible composition series of one of these objects are equivalent by the Jordan-Hölder theorem. One class of these has locally Euclidean structure and is named for Lie [LEE]. Another class of this type of object dictates the solvability of polynomials and is named for Galois [gal-WAH]. As with many algebraic structures, the set of commuting values in one of these is its center and one equal to its own center is Abelian. For 10 points, name these mathemati
Locally compact examples of these algebraic structures can be assigned Haar measures. All possible composition series of one of these objects are equivalent by the Jordan-Hölder theorem. One class of these has locally Euclidean structure and is named for Lie [LEE]. Another class of this type of object dictates the solvability of polynomials and is named for Galois [gal-WAH]. As with many algebraic structures, the set of commuting values in one of these is its center and one equal to its own center is Abelian. For 10 points, name these mathematical structures, each of which consists of a set endowed an associated operation for which there exist an identity and inverses.
Locally compact examples of these algebraic structures can be assigned Haar measures.
{groups}