Mathematics. A system of groups of elements, each of the groups being formed of a certain number of elements, so that each occurs exactly a given…
| 单词 | θ114951 |
| 释义 | the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > set > in abstract algebra > groups (23) syntheme1844 Mathematics. A system of groups of elements, each of the groups being formed of a certain number of elements, so that each occurs exactly a given… group1854 Mathematics. Originally: a set of operations so constituted that the product of any number of these operations is always itself a member of the… substitution group1861 = permutation group n. at permutation, n. compounds 2. quaternion group1881 the group which is formed under multiplication by the unit quaternions, 1, i, j, and k, and their negatives. subgroup1881 Mathematics. A group all of whose elements are elements of some group G and subject to the same operations as G. Abelian group1892 a group whose binary operation is commutative. permutation group1893 a group whose elements are permutations; = substitution group n. at substitution, n. compounds. quotient group1893 = factor group n. at factor, n. compounds 2. factor group1895 a group G/N, the elements of which are the cosets in a given group G of a normal subgroup N of G; also called quotient group. order1897 Mathematics. The smallest positive integer m for which g m is equal to the identity element of a group, g being any given element of the group. symmetric group1897 the group of all the permutations of a set of unlike entities. point group1903 A group of symmetry operations that leave unmoved at least one point within the object to which they apply; spec. any of thirty-two sets of… Sylow subgroup1905 Used attributively and in the possessive to designate concepts in group theory propounded by Sylow (Ma… a subgroup whose order is the largest… module1927 Mathematics. Originally: a set that is a subset of a ring and is closed under addition and subtraction. Now usually: a commutative additive group… Lie group1939 Used attributively to denote certain concepts investigated by Lie. a topological group in which it is possible to label the group elements by a… symmetry group1956 a group (group, n. 7) whose elements are all the symmetry operations of a particular entity. Weyl group1961 Used attributively to designate various concepts introduced by Weyl. a quotient group, important in the study of simple groups, constructed from two… stabilizer1965 Mathematics. A subgroup of a permutation group, being the group of elements that map some subset of the permuted elements on to itself. Subcategories:— quality (4) — quantity (1) |
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